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+# Linear Algebra - Master Plan
+
+## 🎯 Goal: Linear Algebra Mastery
+
+This comprehensive plan will guide you from basic vector concepts to advanced linear algebra applications in machine learning, computer graphics, data science, and quantum computing.
+
+## 📊 Learning Journey Overview
+
+**Total Duration:** 6-10 months (depending on pace and mathematical background)
+**Target Level:** Advanced Linear Algebra with Applications
+**Daily Commitment:** 1-2 hours recommended
+**Prerequisites:** High school algebra (recommended but not required)
+
+## 🗺️ Learning Path Structure
+
+```
+Phase 1: Foundations (1.5-2 months)
+    └─> Vectors, Matrices, Basic Operations
+    
+Phase 2: Core Theory (2-3 months)
+    └─> Systems of Equations, Matrix Decompositions, Eigenvalues
+    
+Phase 3: Advanced Topics (1.5-2 months)
+    └─> Vector Spaces, Linear Transformations, Orthogonality
+    
+Phase 4: Applications (1-2 months)
+    └─> Machine Learning, Graphics, Data Science, Optimization
+    
+Phase 5: Specialization (Ongoing)
+    └─> Choose your domain (ML, Graphics, Quantum, Data Science)
+```
+
+## 📚 Learning Modules Breakdown
+
+### Phase 1: Linear Algebra Foundations (Beginner)
+**Duration:** 1.5-2 months | **Difficulty:** ⭐⭐☆☆☆
+
+1. **Module 1.1: Vectors Basics** (2 weeks)
+   - Vector Definition & Notation
+   - Vector Components
+   - Geometric Interpretation (2D, 3D)
+   - Vector Addition & Subtraction
+   - Scalar Multiplication
+   - Zero Vector & Unit Vectors
+   - Standard Basis Vectors (i, j, k)
+   - Linear Combinations
+
+2. **Module 1.2: Dot Product & Vector Operations** (2 weeks)
+   - Dot Product (Inner Product)
+   - Geometric Interpretation
+   - Angle Between Vectors
+   - Vector Length (Magnitude/Norm)
+   - Distance Between Vectors
+   - Orthogonal Vectors
+   - Vector Projection
+   - Cross Product (3D)
+
+3. **Module 1.3: Matrices Basics** (2 weeks)
+   - Matrix Definition & Notation
+   - Matrix Dimensions (m × n)
+   - Special Matrices (Identity, Zero, Diagonal)
+   - Matrix Addition & Subtraction
+   - Scalar Multiplication
+   - Matrix Multiplication
+   - Transpose
+   - Matrix Powers
+
+4. **Module 1.4: Matrix Properties** (1 week)
+   - Symmetric Matrices
+   - Antisymmetric Matrices
+   - Triangular Matrices (Upper/Lower)
+   - Trace of a Matrix
+   - Matrix Norms
+   - Matrix Multiplication Properties
+   - Non-commutativity
+   - Associativity & Distributivity
+
+---
+
+### Phase 2: Core Linear Algebra (Intermediate)
+**Duration:** 2-3 months | **Difficulty:** ⭐⭐⭐☆☆
+
+5. **Module 2.1: Systems of Linear Equations** (2 weeks)
+   - Linear Equation Systems
+   - Matrix Representation (Ax = b)
+   - Gaussian Elimination
+   - Row Echelon Form (REF)
+   - Reduced Row Echelon Form (RREF)
+   - Back Substitution
+   - Consistency & Inconsistency
+   - Homogeneous Systems
+
+6. **Module 2.2: Matrix Inverses** (2 weeks)
+   - Inverse Matrix Definition
+   - Properties of Inverses
+   - Computing Inverses (Gauss-Jordan)
+   - Invertible vs Singular Matrices
+   - Inverse of Products
+   - Inverse and Transpose Relationship
+   - Solving Systems with Inverses
+   - Computational Considerations
+
+7. **Module 2.3: Determinants** (2 weeks)
+   - Determinant Definition
+   - 2×2 and 3×3 Determinants
+   - Cofactor Expansion
+   - Properties of Determinants
+   - Determinant and Invertibility
+   - Determinant of Products
+   - Cramer's Rule
+   - Geometric Interpretation (Volume)
+
+8. **Module 2.4: Vector Spaces** (3 weeks)
+   - Vector Space Definition
+   - Subspaces
+   - Span of Vectors
+   - Linear Independence
+   - Linear Dependence
+   - Basis and Dimension
+   - Coordinate Systems
+   - Change of Basis
+
+9. **Module 2.5: Linear Transformations** (2 weeks)
+   - Transformation Definition
+   - Matrix Representation
+   - Kernel (Null Space)
+   - Range (Column Space)
+   - Rank-Nullity Theorem
+   - One-to-one & Onto
+   - Isomorphisms
+   - Composition of Transformations
+
+10. **Module 2.6: Eigenvalues & Eigenvectors** (3 weeks)
+    - Eigenvalue Definition
+    - Eigenvector Definition
+    - Characteristic Polynomial
+    - Computing Eigenvalues
+    - Computing Eigenvectors
+    - Eigenspaces
+    - Diagonalization
+    - Similar Matrices
+    - Algebraic vs Geometric Multiplicity
+
+---
+
+### Phase 3: Advanced Linear Algebra
+**Duration:** 1.5-2 months | **Difficulty:** ⭐⭐⭐⭐☆
+
+11. **Module 3.1: Orthogonality** (2 weeks)
+    - Orthogonal Vectors
+    - Orthogonal Complement
+    - Orthogonal Basis
+    - Orthonormal Basis
+    - Gram-Schmidt Process
+    - QR Decomposition
+    - Orthogonal Matrices
+    - Orthogonal Projections
+
+12. **Module 3.2: Inner Product Spaces** (2 weeks)
+    - Inner Product Definition
+    - Inner Product Properties
+    - Cauchy-Schwarz Inequality
+    - Triangle Inequality
+    - Norm from Inner Product
+    - Orthogonality in Inner Product Spaces
+    - Best Approximation
+    - Least Squares Problems
+
+13. **Module 3.3: Matrix Decompositions** (3 weeks)
+    - LU Decomposition
+    - QR Decomposition (revisited)
+    - Cholesky Decomposition
+    - Singular Value Decomposition (SVD)
+    - Spectral Theorem
+    - Jordan Normal Form
+    - Polar Decomposition
+    - Applications of Decompositions
+
+14. **Module 3.4: Norms & Conditioning** (1 week)
+    - Vector Norms (L1, L2, L∞)
+    - Matrix Norms
+    - Frobenius Norm
+    - Operator Norm
+    - Condition Number
+    - Numerical Stability
+    - Ill-conditioned Problems
+    - Error Analysis
+
+---
+
+### Phase 4: Applications (Advanced)
+**Duration:** 1-2 months | **Difficulty:** ⭐⭐⭐⭐☆
+
+15. **Module 4.1: Linear Algebra in Machine Learning** (2 weeks)
+    - Data Representation (Feature Vectors)
+    - Linear Regression
+    - Principal Component Analysis (PCA)
+    - Dimensionality Reduction
+    - Singular Value Decomposition in ML
+    - Recommender Systems
+    - Neural Network Foundations
+    - Backpropagation Math
+
+16. **Module 4.2: Computer Graphics Applications** (2 weeks)
+    - Homogeneous Coordinates
+    - Transformation Matrices (Translation, Rotation, Scaling)
+    - 3D Graphics Pipeline
+    - Camera Matrices
+    - Projection Matrices
+    - Quaternions (Rotation)
+    - Lighting & Shading Math
+    - Ray Tracing Fundamentals
+
+17. **Module 4.3: Optimization & Numerical Methods** (2 weeks)
+    - Gradient Descent
+    - Convex Optimization
+    - Lagrange Multipliers
+    - Newton's Method
+    - Iterative Methods (Jacobi, Gauss-Seidel)
+    - Conjugate Gradient Method
+    - Power Iteration
+    - Krylov Subspace Methods
+
+18. **Module 4.4: Data Science Applications** (1 week)
+    - Covariance Matrices
+    - Correlation Analysis
+    - Linear Models
+    - Feature Scaling & Normalization
+    - Dimensionality Reduction
+    - Matrix Factorization
+    - Network Analysis (Graphs as Matrices)
+    - Markov Chains
+
+---
+
+### Phase 5: Specializations (Choose Your Path)
+**Duration:** Ongoing | **Difficulty:** ⭐⭐⭐⭐⭐
+
+19. **Specialization A: Machine Learning Deep Dive**
+    - Deep Learning Mathematics
+    - Tensor Operations
+    - Automatic Differentiation
+    - Backpropagation in Detail
+    - Convolutional Neural Networks Math
+    - Recurrent Networks Math
+    - Attention Mechanisms
+    - Optimization Algorithms
+
+20. **Specialization B: Computational Linear Algebra**
+    - Numerical Linear Algebra
+    - Sparse Matrices
+    - Iterative Solvers
+    - Parallel Matrix Algorithms
+    - GPU Computing for Linear Algebra
+    - BLAS & LAPACK Libraries
+    - Floating Point Arithmetic
+    - Stability & Accuracy
+
+21. **Specialization C: Quantum Computing**
+    - Quantum States (Vectors in Hilbert Space)
+    - Bra-ket Notation
+    - Quantum Gates (Unitary Matrices)
+    - Tensor Products
+    - Entanglement
+    - Quantum Circuits
+    - Quantum Algorithms (Grover, Shor)
+    - Quantum Error Correction
+
+22. **Specialization D: Advanced Applications**
+    - Graph Theory & Networks
+    - Control Theory
+    - Signal Processing
+    - Cryptography
+    - Robotics & Kinematics
+    - Finite Element Methods
+    - Image Processing
+    - Computational Physics
+
+---
+
+## 📈 Progress Tracking
+
+### Mastery Levels
+- **Level 0:** Unfamiliar - Never seen the concept
+- **Level 1:** Aware - Basic understanding, can't apply
+- **Level 2:** Competent - Can solve with reference
+- **Level 3:** Proficient - Can solve without reference
+- **Level 4:** Expert - Can teach, prove theorems, apply creatively
+
+### Weekly Goals
+- Complete 1 module every 1-2 weeks
+- Solve 10-15 practice problems daily
+- Prove 2-3 theorems per week
+- Apply concepts in coding (Python/MATLAB)
+- Review previous week's material
+
+### Monthly Assessments
+- Take comprehensive exam covering month's topics
+- Solve applied problems
+- Prove key theorems
+- Implement algorithms
+
+---
+
+## 🎓 Learning Resources
+
+### Essential Textbooks
+1. **"Introduction to Linear Algebra"** by Gilbert Strang - Best intro
+2. **"Linear Algebra Done Right"** by Sheldon Axler - Theoretical
+3. **"Linear Algebra and Its Applications"** by David Lay - Applied
+4. **"Matrix Analysis"** by Horn & Johnson - Advanced
+5. **"Numerical Linear Algebra"** by Trefethen & Bau - Computational
+
+### Video Lectures
+- MIT OCW: Gilbert Strang's Linear Algebra (legendary!)
+- 3Blue1Brown: "Essence of Linear Algebra" (visual intuition)
+- Khan Academy: Linear Algebra series
+- Stanford CS229: Linear Algebra Review
+
+### Online Resources
+- WolframAlpha (matrix calculations)
+- SageMath / SymPy (symbolic computation)
+- MATLAB / Octave (numerical computation)
+- NumPy / SciPy (Python implementation)
+
+### Practice Platforms
+- Math Stack Exchange
+- Brilliant.org (interactive problems)
+- Paul's Online Math Notes
+- MIT OpenCourseWare Problem Sets
+
+---
+
+## 🏆 Milestones & Achievements
+
+### Milestone 1: Vector & Matrix Fundamentals (Month 2)
+- ✅ Master vector operations
+- ✅ Perform matrix arithmetic fluently
+- ✅ Understand geometric interpretations
+- ✅ Compute dot products, cross products, norms
+- 🎯 **Project:** Implement vector/matrix library in Python
+
+### Milestone 2: Linear Systems & Decompositions (Month 4-5)
+- ✅ Solve systems of equations (Gaussian elimination)
+- ✅ Compute matrix inverses and determinants
+- ✅ Understand eigenvalues and eigenvectors
+- ✅ Apply basic decompositions (LU, QR)
+- 🎯 **Project:** Linear equation solver
+
+### Milestone 3: Abstract Vector Spaces (Month 6-7)
+- ✅ Work with abstract vector spaces
+- ✅ Understand linear transformations
+- ✅ Apply orthogonalization (Gram-Schmidt)
+- ✅ Master SVD and applications
+- 🎯 **Project:** Image compression using SVD
+
+### Milestone 4: Applications Mastery (Month 8-9)
+- ✅ Apply to machine learning (PCA, regression)
+- ✅ Implement graphics transformations
+- ✅ Solve optimization problems
+- ✅ Work with real-world data
+- 🎯 **Project:** Build ML model or graphics engine component
+
+### Milestone 5: Specialization (Month 10+)
+- ✅ Deep expertise in chosen domain
+- ✅ Advanced applications
+- ✅ Research-level understanding
+- 🎯 **Project:** Advanced application in specialization
+
+---
+
+## 📝 Assessment Strategy
+
+### Weekly Problem Sets
+- 15-20 computational problems
+- 3-5 proof-based problems
+- Mix of routine & challenging
+- Self-graded with solutions
+
+### Monthly Exams
+- 20-30 problems
+- Mix: Computation (60%), Theory (20%), Applications (20%)
+- "I don't know" option available
+- Automatic grading for computational problems
+
+### Project Assessments
+- Implement algorithms
+- Apply to real problems
+- Code review
+- Mathematical correctness
+
+---
+
+## 🚀 Getting Started
+
+### Week 1 Action Plan
+1. Review basic algebra if needed
+2. Set up computation tools (Python + NumPy, or MATLAB)
+3. Watch 3Blue1Brown: "Essence of Linear Algebra" (first 3 videos)
+4. Start Module 1.1: Vectors Basics
+5. Solve first 10 vector problems
+6. Take first quiz
+
+### Daily Study Routine
+- **Theory (30-40 min):** Read textbook, watch lectures
+- **Computation (30-40 min):** Solve numerical problems
+- **Proof (20-30 min):** Work on proof-based problems
+- **Implementation (optional 30 min):** Code in Python/MATLAB
+
+### Weekend Activities
+- Build small projects (vector calculator, matrix solver)
+- Watch 3Blue1Brown videos for visual intuition
+- Solve challenging problems
+- Review week's material
+
+---
+
+## 💡 Learning Tips
+
+1. **Visualize Everything:** Linear algebra is geometric - draw it!
+2. **Prove Key Theorems:** Understanding proofs builds deep intuition
+3. **Implement in Code:** Programming solidifies understanding
+4. **Use Multiple Resources:** Different explanations help
+5. **Work Many Problems:** Fluency requires practice
+6. **Connect to Applications:** See why it matters
+7. **Start Geometric, Then Abstract:** Intuition first, formalism later
+8. **Review Regularly:** Spaced repetition is key
+
+---
+
+## 🔗 Integration with Programming
+
+### Python Implementation
+Use NumPy for all concepts:
+- `numpy.array()` for vectors/matrices
+- `numpy.dot()` for dot product
+- `numpy.linalg` for decompositions
+- `numpy.linalg.eig()` for eigenvalues
+- Visualize with matplotlib
+
+### MATLAB/Octave
+Industry standard for numerical linear algebra:
+- Matrix operations built-in
+- Efficient computation
+- Rich visualization
+- Used in research and industry
+
+### Applications
+- Machine learning libraries (scikit-learn, TensorFlow)
+- Graphics libraries (OpenGL matrices)
+- Data science (pandas, scipy)
+- Optimization (cvxpy, scipy.optimize)
+
+---
+
+## 🎯 Course Outline Detail
+
+### Phase 1: Foundations (1.5-2 months)
+
+#### Module 1.1: Vectors Basics
+**Concepts:**
+- Vectors in ℝⁿ
+- Geometric representation
+- Vector arithmetic
+- Linear combinations
+
+**Key Skills:**
+- Visualize vectors in 2D/3D
+- Add/subtract vectors geometrically and algebraically
+- Compute scalar multiples
+- Express vectors as linear combinations
+
+**Problems:** 30-40 practice problems
+
+---
+
+#### Module 1.2: Dot Product & Vector Operations
+**Concepts:**
+- Dot product: a · b = Σ aᵢbᵢ
+- Angle: cos(θ) = (a · b) / (||a|| ||b||)
+- Orthogonality: a ⊥ b ⟺ a · b = 0
+- Projection: proj_b(a) = ((a · b) / ||b||²) b
+
+**Key Skills:**
+- Compute dot products
+- Find angles between vectors
+- Test orthogonality
+- Project vectors
+- Compute cross products (3D)
+
+**Problems:** 40-50 practice problems
+
+---
+
+#### Module 1.3: Matrices Basics
+**Concepts:**
+- Matrix as array of numbers
+- Matrix multiplication: (AB)ᵢⱼ = Σ AᵢₖBₖⱼ
+- Identity matrix: AI = IA = A
+- Transpose: (Aᵀ)ᵢⱼ = Aⱼᵢ
+
+**Key Skills:**
+- Add/subtract matrices
+- Multiply matrices correctly
+- Compute transposes
+- Work with special matrices
+
+**Problems:** 50-60 practice problems
+
+---
+
+### Phase 2: Core Theory (2-3 months)
+
+#### Module 2.1: Systems of Linear Equations
+**Concepts:**
+- Ax = b representation
+- Gaussian elimination algorithm
+- Row operations
+- Existence and uniqueness of solutions
+
+**Key Skills:**
+- Solve systems using Gaussian elimination
+- Determine consistency
+- Find all solutions (unique, infinite, none)
+- Interpret geometrically
+
+**Problems:** 40-50 systems to solve
+
+---
+
+#### Module 2.6: Eigenvalues & Eigenvectors
+**Concepts:**
+- Av = λv (defining equation)
+- det(A - λI) = 0 (characteristic equation)
+- Eigenspace for each eigenvalue
+- Diagonalization: A = PDP⁻¹
+
+**Key Skills:**
+- Find eigenvalues (solve characteristic polynomial)
+- Find eigenvectors (solve (A - λI)v = 0)
+- Diagonalize matrices
+- Apply to differential equations, Markov chains
+
+**Problems:** 30-40 eigenvalue problems
+
+---
+
+### Phase 3: Advanced Topics (1.5-2 months)
+
+#### Module 3.1: Orthogonality
+**Concepts:**
+- Orthogonal sets
+- Orthonormal bases
+- Gram-Schmidt process
+- QR decomposition: A = QR
+
+**Key Skills:**
+- Create orthonormal bases
+- Apply Gram-Schmidt
+- Compute QR decomposition
+- Solve least squares: Ax ≈ b
+
+**Problems:** 25-30 orthogonalization problems
+
+---
+
+#### Module 3.3: Matrix Decompositions
+**Concepts:**
+- SVD: A = UΣVᵀ
+- Applications: Image compression, recommender systems
+- Spectral decomposition: A = QΛQᵀ
+- Low-rank approximations
+
+**Key Skills:**
+- Compute SVD
+- Use SVD for compression
+- Apply to data analysis
+- Solve ill-conditioned problems
+
+**Problems:** 20-25 decomposition problems
+
+---
+
+### Phase 4: Applications (1-2 months)
+
+#### Module 4.1: Machine Learning
+**Concepts:**
+- Linear regression: θ = (XᵀX)⁻¹Xᵀy
+- PCA: eigenvectors of covariance matrix
+- Neural networks: matrix multiplications
+- Gradient descent: direction of steepest descent
+
+**Key Skills:**
+- Implement linear regression
+- Apply PCA for dimensionality reduction
+- Understand neural network math
+- Optimize using gradients
+
+**Projects:**
+- Linear regression from scratch
+- PCA implementation
+- Simple neural network
+
+---
+
+## 📊 Topics Coverage Matrix
+
+### Computational Topics (60%)
+- Matrix operations and arithmetic
+- Solving linear systems
+- Computing inverses and determinants
+- Eigenvalue/eigenvector computation
+- Matrix decompositions
+- Numerical methods
+
+### Theoretical Topics (25%)
+- Vector space theory
+- Linear transformations
+- Basis and dimension
+- Rank-nullity theorem
+- Spectral theory
+- Proofs and theorems
+
+### Applied Topics (15%)
+- Machine learning applications
+- Computer graphics
+- Optimization
+- Data analysis
+- Real-world problem solving
+
+---
+
+## 🎓 Recommended Study Paths
+
+### Path A: Theory-First (Pure Mathematics Background)
+1. Start with abstract definitions
+2. Prove theorems rigorously
+3. Then see applications
+4. Focus on "Linear Algebra Done Right" by Axler
+
+### Path B: Computation-First (Engineering/CS Background) ⭐ RECOMMENDED
+1. Start with vectors and matrices
+2. Learn through computation
+3. Build geometric intuition
+4. Then add rigor
+5. Focus on Gilbert Strang's materials
+
+### Path C: Application-Driven (Data Science/ML Focus)
+1. Start with applications (ML, graphics)
+2. Learn theory as needed
+3. Heavy Python/NumPy usage
+4. Focus on David Lay's book
+
+---
+
+## 📐 Mathematical Prerequisites
+
+### Required (High School Level)
+- Basic algebra (equations, polynomials)
+- Functions and graphing
+- Arithmetic operations
+
+### Helpful But Not Required
+- Calculus (for some applications)
+- Proof techniques (for theoretical parts)
+- Programming (for computational practice)
+
+### Will Learn From Scratch
+- All linear algebra concepts
+- Mathematical notation
+- Proof methods (as needed)
+- Computational techniques
+
+---
+
+## 💻 Computational Tools
+
+### Recommended: Python + NumPy
+```python
+import numpy as np
+import matplotlib.pyplot as plt
+
+# Create vectors
+v = np.array([1, 2, 3])
+w = np.array([4, 5, 6])
+
+# Dot product
+dot = np.dot(v, w)
+
+# Matrix operations
+A = np.array([[1, 2], [3, 4]])
+B = np.linalg.inv(A)  # Inverse
+eigs = np.linalg.eig(A)  # Eigenvalues
+
+# SVD
+U, S, Vt = np.linalg.svd(A)
+```
+
+### Alternative: MATLAB/Octave
+- Industry standard
+- Built for matrix computation
+- Rich toolboxes
+- Used in academia and industry
+
+### Visualization: 3Blue1Brown Style
+- matplotlib (Python)
+- manim (Python animation)
+- GeoGebra (interactive)
+- Desmos (2D graphing)
+
+---
+
+## 🏆 Success Metrics
+
+### Knowledge Metrics
+- Can solve 90% of computational problems correctly
+- Can prove 70% of key theorems
+- Understand geometric meaning of all operations
+- Can implement algorithms efficiently
+
+### Application Metrics
+- Build working ML models
+- Implement graphics transformations
+- Solve real-world optimization problems
+- Use linear algebra in projects
+
+### Fluency Metrics
+- Solve standard problems in <5 minutes
+- Recognize patterns quickly
+- Choose appropriate methods
+- Debug matrix computations
+
+---
+
+## 🔗 Next Steps
+
+1. Review detailed modules in `01_KNOWLEDGE_GRAPH.md`
+2. Assess your level in `02_INITIAL_ASSESSMENT.md`
+3. Set up Python + NumPy or MATLAB
+4. Watch 3Blue1Brown's series (11 videos)
+5. Start Module 1.1: Vectors Basics
+
+---
+
+## 📊 Estimated Timeline by Background
+
+### No Math Background (Starting Fresh)
+- **Phase 1:** 2-3 months
+- **Phase 2:** 3-4 months
+- **Phase 3:** 2-3 months
+- **Phase 4:** 2 months
+- **Total:** 9-12 months to applications
+
+### Some Math Background (Algebra comfortable)
+- **Phase 1:** 1.5-2 months
+- **Phase 2:** 2-3 months
+- **Phase 3:** 1.5-2 months
+- **Phase 4:** 1-2 months
+- **Total:** 6-9 months to applications
+
+### Strong Math Background (Calculus/Proofs)
+- **Phase 1:** 3-4 weeks (rapid review)
+- **Phase 2:** 2 months
+- **Phase 3:** 1.5 months
+- **Phase 4:** 1 month
+- **Total:** 4-6 months to specialization
+
+---
+
+## 🌟 Why Learn Linear Algebra?
+
+### Foundation for Advanced Fields
+- **Machine Learning:** PCA, neural networks, optimization
+- **Computer Graphics:** All transformations are matrices
+- **Data Science:** Dimensionality reduction, analysis
+- **Quantum Computing:** States are vectors, gates are matrices
+- **Optimization:** All modern optimization uses linear algebra
+- **Physics:** Quantum mechanics, relativity
+
+### Practical Applications
+- Build ML models
+- Create graphics engines
+- Analyze large datasets
+- Solve engineering problems
+- Understand modern AI
+
+### Career Opportunities
+- Data Scientist
+- Machine Learning Engineer
+- Computer Graphics Programmer
+- Quantitative Analyst
+- Research Scientist
+- Robotics Engineer
+
+---
+
+**Remember:** Linear Algebra is the language of modern mathematics, science, and technology. Master it and unlock countless opportunities! 📐🚀
+
--- a/learning_plans/linear_algebra/01_KNOWLEDGE_GRAPH.md
+++ b/learning_plans/linear_algebra/01_KNOWLEDGE_GRAPH.md
@@ -0,0 +1,709 @@
+# Linear Algebra Knowledge Graph - Complete Dependency Map
+
+## 🌳 Knowledge Tree Structure
+
+This document maps all Linear Algebra concepts with their dependencies and optimal learning order.
+
+---
+
+## Level 1: Foundation Concepts (No Prerequisites)
+
+### 1.1 Basic Algebra Review
+```
+┌──────────────────────────────┐
+│ Arithmetic Operations        │
+│ - Addition, Subtraction      │
+│ - Multiplication, Division   │
+│ - Order of operations        │
+└──────────────────────────────┘
+        │
+        ├─> Algebraic Expressions
+        ├─> Solving Linear Equations
+        ├─> Polynomials
+        └─> Summation Notation (Σ)
+```
+
+### 1.2 Coordinate Systems
+```
+┌──────────────────────────────┐
+│ Cartesian Coordinates        │
+│ - 2D plane (x, y)           │
+│ - 3D space (x, y, z)        │
+│ - Points and plotting       │
+└──────────────────────────────┘
+        │
+        ├─> Distance Formula
+        ├─> Midpoint Formula
+        └─> Graphing Functions
+```
+
+---
+
+## Level 2: Vectors - Geometric (Requires Level 1)
+
+### 2.1 Vector Basics
+```
+┌──────────────────────────────┐
+│ Vector Definition            │
+│ - Magnitude and Direction   │
+│ - Component Form            │
+│ - Position Vectors          │
+└──────────────────────────────┘
+        │
+        ├─> Vector Notation (bold, arrow)
+        ├─> ℝ² and ℝ³ vectors
+        ├─> n-dimensional vectors (ℝⁿ)
+        └─> Column vs Row Vectors
+
+┌──────────────────────────────┐
+│ Vector Visualization         │
+│ - Geometric arrows          │
+│ - Head and tail             │
+│ - Parallel vectors          │
+└──────────────────────────────┘
+```
+
+### 2.2 Vector Operations (Geometric)
+```
+┌──────────────────────────────┐
+│ Vector Addition              │
+│ - Parallelogram Rule        │
+│ - Tip-to-tail Method        │
+│ - Component-wise Addition   │
+└──────────────────────────────┘
+        │
+        ├─> Vector Subtraction
+        ├─> Scalar Multiplication (Scaling)
+        ├─> Linear Combinations
+        └─> Zero Vector
+
+┌──────────────────────────────┐
+│ Special Vectors              │
+│ - Unit Vectors              │
+│ - Standard Basis (i, j, k)  │
+│ - Normalization             │
+└──────────────────────────────┘
+```
+
+---
+
+## Level 3: Vector Products (Requires Level 2)
+
+### 3.1 Dot Product (Inner Product)
+```
+┌──────────────────────────────┐
+│ Dot Product                  │
+│ - a · b = Σ aᵢbᵢ           │
+│ - a · b = ||a|| ||b|| cos θ│
+│ - Scalar result             │
+└──────────────────────────────┘
+        │
+        ├─> Vector Length (Norm): ||v|| = √(v · v)
+        ├─> Distance: ||a - b||
+        ├─> Angle Between Vectors
+        ├─> Orthogonality (a · b = 0)
+        ├─> Vector Projection
+        └─> Cauchy-Schwarz Inequality
+
+┌──────────────────────────────┐
+│ Properties of Dot Product    │
+│ - Commutative: a · b = b · a│
+│ - Distributive              │
+│ - Linearity                 │
+└──────────────────────────────┘
+```
+
+### 3.2 Cross Product (3D Only)
+```
+┌──────────────────────────────┐
+│ Cross Product (a × b)        │
+│ - Vector result             │
+│ - Perpendicular to both     │
+│ - Right-hand rule           │
+└──────────────────────────────┘
+        │
+        ├─> Magnitude: ||a × b|| = ||a|| ||b|| sin θ
+        ├─> Area of Parallelogram
+        ├─> Determinant Form
+        ├─> Anti-commutative: a × b = -(b × a)
+        └─> Triple Scalar Product
+
+┌──────────────────────────────┐
+│ Applications                 │
+│ - Normal vectors            │
+│ - Torque calculations       │
+│ - Area and volume           │
+└──────────────────────────────┘
+```
+
+---
+
+## Level 4: Matrices - Basics (Requires Level 2-3)
+
+### 4.1 Matrix Fundamentals
+```
+┌──────────────────────────────┐
+│ Matrix Definition            │
+│ - m × n array of numbers    │
+│ - Rows and columns          │
+│ - Matrix indexing Aᵢⱼ       │
+└──────────────────────────────┘
+        │
+        ├─> Matrix Addition/Subtraction
+        ├─> Scalar Multiplication
+        ├─> Transpose (Aᵀ)
+        ├─> Special Matrices (I, O, Diagonal)
+        └─> Matrix Equality
+```
+
+### 4.2 Matrix Multiplication
+```
+┌──────────────────────────────┐
+│ Matrix Product              │
+│ - (AB)ᵢⱼ = Σ AᵢₖBₖⱼ        │
+│ - Dimension compatibility   │
+│ - Non-commutative           │
+└──────────────────────────────┘
+        │
+        ├─> Properties (Associative, Distributive)
+        ├─> Identity: AI = IA = A
+        ├─> Matrix Powers: A², A³, ...
+        ├─> Matrix as Linear Transformation
+        └─> Block Matrix Multiplication
+```
+
+---
+
+## Level 5: Linear Systems (Requires Level 4)
+
+### 5.1 Systems of Linear Equations
+```
+┌──────────────────────────────┐
+│ System Representation        │
+│ - Ax = b                    │
+│ - Augmented Matrix [A|b]    │
+│ - Coefficient Matrix        │
+└──────────────────────────────┘
+        │
+        ├─> Gaussian Elimination
+        ├─> Row Operations
+        ├─> Row Echelon Form (REF)
+        ├─> Reduced Row Echelon Form (RREF)
+        └─> Back Substitution
+
+┌──────────────────────────────┐
+│ Solution Types               │
+│ - Unique Solution           │
+│ - Infinite Solutions        │
+│ - No Solution               │
+└──────────────────────────────┘
+        │
+        ├─> Consistency
+        ├─> Homogeneous Systems
+        ├─> Parametric Solutions
+        └─> Geometric Interpretation
+```
+
+---
+
+## Level 6: Matrix Inverses & Determinants (Requires Level 5)
+
+### 6.1 Matrix Inverse
+```
+┌──────────────────────────────┐
+│ Inverse Definition           │
+│ - AA⁻¹ = A⁻¹A = I          │
+│ - Exists iff det(A) ≠ 0     │
+│ - Unique if exists          │
+└──────────────────────────────┘
+        │
+        ├─> Computing Inverses (Gauss-Jordan)
+        ├─> Inverse Properties: (AB)⁻¹ = B⁻¹A⁻¹
+        ├─> Inverse and Transpose: (Aᵀ)⁻¹ = (A⁻¹)ᵀ
+        ├─> Solving Systems: x = A⁻¹b
+        └─> Invertible Matrix Theorem
+```
+
+### 6.2 Determinants
+```
+┌──────────────────────────────┐
+│ Determinant                  │
+│ - det(A) or |A|             │
+│ - Scalar value              │
+│ - Invertibility test        │
+└──────────────────────────────┘
+        │
+        ├─> 2×2: ad - bc
+        ├─> 3×3: Rule of Sarrus or Cofactor
+        ├─> n×n: Cofactor Expansion
+        ├─> Properties: det(AB) = det(A)det(B)
+        ├─> det(Aᵀ) = det(A)
+        ├─> Row Operations Effect
+        ├─> Cramer's Rule
+        └─> Geometric Meaning (Area/Volume)
+```
+
+---
+
+## Level 7: Vector Spaces (Requires Level 2-6)
+
+### 7.1 Abstract Vector Spaces
+```
+┌──────────────────────────────┐
+│ Vector Space Definition      │
+│ - 10 Axioms                 │
+│ - Closure under + and ·     │
+│ - Examples: ℝⁿ, Polynomials │
+└──────────────────────────────┘
+        │
+        ├─> Subspaces
+        ├─> Span of Vectors
+        ├─> Linear Independence
+        ├─> Linear Dependence
+        ├─> Basis
+        └─> Dimension
+
+┌──────────────────────────────┐
+│ Important Subspaces          │
+│ - Null Space (Kernel)       │
+│ - Column Space (Range)      │
+│ - Row Space                 │
+│ - Left Null Space           │
+└──────────────────────────────┘
+        │
+        ├─> Rank of Matrix
+        ├─> Nullity of Matrix
+        ├─> Rank-Nullity Theorem
+        └─> Fundamental Theorem of Linear Algebra
+```
+
+### 7.2 Basis & Dimension
+```
+┌──────────────────────────────┐
+│ Basis                        │
+│ - Linearly independent      │
+│ - Spans the space           │
+│ - Minimum spanning set      │
+└──────────────────────────────┘
+        │
+        ├─> Standard Basis
+        ├─> Dimension = # basis vectors
+        ├─> Change of Basis
+        ├─> Coordinates Relative to Basis
+        └─> Uniqueness of Dimension
+```
+
+---
+
+## Level 8: Linear Transformations (Requires Level 7)
+
+### 8.1 Linear Transformations
+```
+┌──────────────────────────────┐
+│ Transformation T: V → W      │
+│ - T(u + v) = T(u) + T(v)    │
+│ - T(cv) = cT(v)             │
+│ - Matrix representation     │
+└──────────────────────────────┘
+        │
+        ├─> Kernel (Null Space): ker(T) = {v : T(v) = 0}
+        ├─> Range (Image): range(T) = {T(v) : v ∈ V}
+        ├─> Rank-Nullity Theorem
+        ├─> One-to-one Transformations
+        ├─> Onto Transformations
+        └─> Isomorphisms
+
+┌──────────────────────────────┐
+│ Standard Transformations     │
+│ - Rotation                  │
+│ - Reflection                │
+│ - Projection                │
+│ - Scaling                   │
+└──────────────────────────────┘
+        │
+        └─> Composition of Transformations
+```
+
+---
+
+## Level 9: Eigenvalues & Eigenvectors (Requires Level 6-8)
+
+### 9.1 Eigen-Theory
+```
+┌──────────────────────────────┐
+│ Eigenvalue Problem           │
+│ - Av = λv                   │
+│ - Characteristic Polynomial │
+│ - det(A - λI) = 0           │
+└──────────────────────────────┘
+        │
+        ├─> Computing Eigenvalues
+        ├─> Computing Eigenvectors
+        ├─> Eigenspace
+        ├─> Algebraic Multiplicity
+        ├─> Geometric Multiplicity
+        └─> Diagonalization
+
+┌──────────────────────────────┐
+│ Diagonalization              │
+│ - A = PDP⁻¹                 │
+│ - D diagonal (eigenvalues)  │
+│ - P columns (eigenvectors)  │
+└──────────────────────────────┘
+        │
+        ├─> Diagonalizable Matrices
+        ├─> Similar Matrices
+        ├─> Powers: Aⁿ = PDⁿP⁻¹
+        └─> Applications: Differential Equations, Markov Chains
+```
+
+---
+
+## Level 10: Orthogonality (Requires Level 3, 7)
+
+### 10.1 Orthogonal Sets
+```
+┌──────────────────────────────┐
+│ Orthogonality                │
+│ - v · w = 0                 │
+│ - Perpendicular vectors     │
+│ - Orthogonal sets           │
+└──────────────────────────────┘
+        │
+        ├─> Orthogonal Basis
+        ├─> Orthonormal Basis
+        ├─> Orthogonal Complement
+        └─> Orthogonal Decomposition
+
+┌──────────────────────────────┐
+│ Gram-Schmidt Process         │
+│ - Orthogonalization         │
+│ - Creates orthonormal basis │
+│ - QR Decomposition          │
+└──────────────────────────────┘
+        │
+        └─> Applications: Least Squares, QR Algorithm
+```
+
+### 10.2 Orthogonal Matrices
+```
+┌──────────────────────────────┐
+│ Orthogonal Matrix Q          │
+│ - QᵀQ = QQᵀ = I            │
+│ - Columns orthonormal       │
+│ - Preserves lengths         │
+└──────────────────────────────┘
+        │
+        ├─> Rotation Matrices
+        ├─> Reflection Matrices
+        ├─> det(Q) = ±1
+        └─> Q⁻¹ = Qᵀ
+```
+
+---
+
+## Level 11: Inner Product Spaces (Requires Level 3, 7, 10)
+
+### 11.1 Inner Products
+```
+┌──────────────────────────────┐
+│ Inner Product ⟨u, v⟩         │
+│ - Generalizes dot product   │
+│ - 4 Axioms                  │
+│ - Induces norm & metric     │
+└──────────────────────────────┘
+        │
+        ├─> Cauchy-Schwarz Inequality
+        ├─> Triangle Inequality
+        ├─> Parallelogram Law
+        ├─> Pythagorean Theorem
+        └─> Norm: ||v|| = √⟨v, v⟩
+
+┌──────────────────────────────┐
+│ Applications                 │
+│ - Function spaces           │
+│ - Polynomial inner products │
+│ - Weighted inner products   │
+└──────────────────────────────┘
+```
+
+---
+
+## Level 12: Matrix Decompositions (Requires Level 6, 9, 10)
+
+### 12.1 LU Decomposition
+```
+┌──────────────────────────────┐
+│ LU Factorization             │
+│ - A = LU                    │
+│ - L: Lower triangular       │
+│ - U: Upper triangular       │
+└──────────────────────────────┘
+        │
+        ├─> Existence Conditions
+        ├─> Computing LU
+        ├─> Solving Systems with LU
+        ├─> Computational Efficiency
+        └─> PLU (with Pivoting)
+```
+
+### 12.2 QR Decomposition
+```
+┌──────────────────────────────┐
+│ QR Factorization             │
+│ - A = QR                    │
+│ - Q: Orthogonal             │
+│ - R: Upper triangular       │
+└──────────────────────────────┘
+        │
+        ├─> Gram-Schmidt Method
+        ├─> Householder Reflections
+        ├─> Givens Rotations
+        ├─> Least Squares Solutions
+        └─> QR Algorithm for Eigenvalues
+```
+
+### 12.3 Eigenvalue Decomposition (Spectral)
+```
+┌──────────────────────────────┐
+│ Spectral Decomposition       │
+│ - A = QΛQᵀ                  │
+│ - Symmetric matrices        │
+│ - Real eigenvalues          │
+└──────────────────────────────┘
+        │
+        ├─> Orthogonal Eigenvectors
+        ├─> Spectral Theorem
+        ├─> Applications
+        └─> Positive Definite Matrices
+```
+
+### 12.4 Singular Value Decomposition (SVD)
+```
+┌──────────────────────────────┐
+│ SVD: A = UΣVᵀ                │
+│ - U: Left singular vectors  │
+│ - Σ: Singular values        │
+│ - V: Right singular vectors │
+└──────────────────────────────┘
+        │
+        ├─> Always Exists (any matrix)
+        ├─> Singular Values
+        ├─> Relationship to Eigenvalues
+        ├─> Pseudoinverse (A⁺)
+        ├─> Low-rank Approximation
+        ├─> Image Compression
+        ├─> Data Analysis (PCA)
+        └─> Recommender Systems
+```
+
+---
+
+## Level 13: Advanced Theory (Requires Level 7-12)
+
+### 13.1 Abstract Algebra Connections
+```
+┌──────────────────────────────┐
+│ Algebraic Structures         │
+│ - Groups                    │
+│ - Rings                     │
+│ - Fields                    │
+└──────────────────────────────┘
+        │
+        ├─> Vector Space as Module
+        ├─> Linear Algebra over Fields
+        └─> Quotient Spaces
+```
+
+### 13.2 Norms & Metrics
+```
+┌──────────────────────────────┐
+│ Vector Norms                 │
+│ - L¹ norm: Σ|vᵢ|           │
+│ - L² norm (Euclidean)       │
+│ - L∞ norm: max|vᵢ|         │
+│ - p-norms                   │
+└──────────────────────────────┘
+        │
+        ├─> Matrix Norms
+        ├─> Frobenius Norm
+        ├─> Operator Norm
+        ├─> Condition Number
+        └─> Error Analysis
+
+┌──────────────────────────────┐
+│ Metric Spaces                │
+│ - Distance Function         │
+│ - Metric Properties         │
+│ - Induced by Norms          │
+└──────────────────────────────┘
+```
+
+---
+
+## Level 14: Applications - Machine Learning (Requires All Previous)
+
+### 14.1 ML Fundamentals
+```
+┌──────────────────────────────┐
+│ Linear Regression            │
+│ - Normal Equations          │
+│ - θ = (XᵀX)⁻¹Xᵀy           │
+│ - Least Squares             │
+└──────────────────────────────┘
+        │
+        ├─> Gradient Descent
+        ├─> Ridge Regression (L2)
+        ├─> Lasso Regression (L1)
+        └─> Regularization
+
+┌──────────────────────────────┐
+│ Dimensionality Reduction     │
+│ - PCA (Principal Components)│
+│ - SVD for PCA               │
+│ - Explained Variance        │
+└──────────────────────────────┘
+        │
+        ├─> Eigenfaces
+        ├─> Feature Extraction
+        ├─> Data Visualization
+        └─> Compression
+```
+
+### 14.2 Neural Networks
+```
+┌──────────────────────────────┐
+│ Neural Network Math          │
+│ - Forward Pass: y = Wx + b  │
+│ - Backpropagation           │
+│ - Gradient Computation      │
+└──────────────────────────────┘
+        │
+        ├─> Weight Matrices
+        ├─> Activation Functions
+        ├─> Loss Gradients
+        └─> Optimization (SGD, Adam)
+```
+
+---
+
+## Level 15: Applications - Graphics (Requires Level 4, 8)
+
+### 15.1 Geometric Transformations
+```
+┌──────────────────────────────┐
+│ 2D Transformations           │
+│ - Translation               │
+│ - Rotation                  │
+│ - Scaling                   │
+│ - Shearing                  │
+└──────────────────────────────┘
+        │
+        ├─> Homogeneous Coordinates
+        ├─> Transformation Matrices
+        ├─> Composition
+        └─> Inverse Transformations
+
+┌──────────────────────────────┐
+│ 3D Graphics                  │
+│ - 3D Rotations              │
+│ - View Transformations      │
+│ - Projection (Orthographic) │
+│ - Projection (Perspective)  │
+└──────────────────────────────┘
+        │
+        ├─> Camera Matrices
+        ├─> Model-View-Projection
+        ├─> Quaternions
+        └─> Euler Angles
+```
+
+---
+
+## 🔗 Dependency Map Summary
+
+### Critical Learning Path
+```
+Level 1 (Algebra Review)
+    ↓
+Level 2 (Vectors - Geometric)
+    ↓
+Level 3 (Vector Products)
+    ↓
+Level 4 (Matrices - Basics)
+    ↓
+Level 5 (Linear Systems)
+    ↓
+Level 6 (Inverses & Determinants)
+    ↓
+Level 7 (Vector Spaces) [Theoretical Branch]
+    ↓
+Level 8 (Linear Transformations)
+    ↓
+Level 9 (Eigenvalues) ←─────────┐
+    ↓                           │
+Level 10 (Orthogonality) ───────┤ Can parallelize
+    ↓                           │
+Level 11 (Inner Products) ──────┘
+    ↓
+Level 12 (Decompositions)
+    ↓
+Level 13 (Advanced Theory) ←────┐
+    ↓                           │ Can parallelize
+Level 14 (ML Applications) ─────┤
+    ↓                           │
+Level 15 (Graphics Applications)┘
+```
+
+### Parallel Learning Opportunities
+- Levels 9, 10, 11 can be learned in parallel after Level 8
+- Level 13 (theory) can parallel with Levels 14-15 (applications)
+- Applications (14-15) depend on decompositions but can be learned in any order
+
+---
+
+## 📊 Prerequisite Matrix
+
+| Topic | Must Know First | Can Learn In Parallel |
+|-------|----------------|----------------------|
+| Dot Product | Vector basics | Cross product |
+| Matrices | Vectors | - |
+| Matrix Mult | Matrix basics | Transpose |
+| Linear Systems | Matrix multiplication | - |
+| Determinants | Matrix multiplication | Inverses |
+| Inverses | Determinants, Systems | - |
+| Vector Spaces | Linear systems, Span | - |
+| Eigenvalues | Determinants, Vector spaces | - |
+| Orthogonality | Dot product, Basis | Inner products |
+| SVD | Eigenvalues, Orthogonality | - |
+| PCA | SVD, Statistics basics | - |
+
+---
+
+## 🎯 Learning Strategies
+
+### Geometric First, Then Abstract
+1. Start with 2D/3D vectors (can visualize)
+2. Build geometric intuition
+3. Generalize to n dimensions
+4. Then study abstract theory
+5. Apply to real problems
+
+### Computation Supports Theory
+1. Solve many numerical examples
+2. Use Python/MATLAB to verify
+3. See patterns emerge
+4. Then learn why (proofs)
+5. Deepen understanding
+
+### Applications Motivate Learning
+1. See where linear algebra is used
+2. Understand why we need it
+3. Learn concepts to solve problems
+4. Apply immediately
+5. Build projects
+
+---
+
+This knowledge graph ensures you build strong foundations before tackling abstract concepts and applications!
+
--- a/learning_plans/linear_algebra/02_INITIAL_ASSESSMENT.md
+++ b/learning_plans/linear_algebra/02_INITIAL_ASSESSMENT.md
@@ -0,0 +1,307 @@
+# Linear Algebra Initial Assessment
+
+## 🎯 Purpose
+
+This assessment will help determine your current Linear Algebra proficiency level and create a personalized learning path.
+
+## 📋 Assessment Structure
+
+### Part 1: Self-Assessment Questionnaire
+### Part 2: Computational Problems
+### Part 3: Knowledge Gap Analysis
+
+---
+
+## Part 1: Self-Assessment Questionnaire
+
+Rate yourself honestly (0-4):
+- **Level 0:** Never heard of it
+- **Level 1:** Basic awareness
+- **Level 2:** Can use with reference
+- **Level 3:** Proficient, confident
+- **Level 4:** Expert, can teach
+
+### Vectors
+| Topic | Level (0-4) | Notes |
+|-------|-------------|-------|
+| Vector definition & notation | | |
+| Vector addition/subtraction | | |
+| Scalar multiplication | | |
+| Dot product | | |
+| Cross product (3D) | | |
+| Vector magnitude/norm | | |
+| Unit vectors | | |
+| Orthogonal vectors | | |
+| Vector projection | | |
+| Linear combinations | | |
+
+### Matrices
+| Topic | Level (0-4) | Notes |
+|-------|-------------|-------|
+| Matrix definition | | |
+| Matrix addition/subtraction | | |
+| Matrix multiplication | | |
+| Transpose | | |
+| Identity matrix | | |
+| Inverse matrix | | |
+| Determinants | | |
+| Special matrices (diagonal, symmetric) | | |
+
+### Linear Systems
+| Topic | Level (0-4) | Notes |
+|-------|-------------|-------|
+| Systems of linear equations | | |
+| Gaussian elimination | | |
+| Row echelon form | | |
+| RREF | | |
+| Solution types (unique, infinite, none) | | |
+| Homogeneous systems | | |
+| Augmented matrices | | |
+
+### Vector Spaces
+| Topic | Level (0-4) | Notes |
+|-------|-------------|-------|
+| Vector space definition | | |
+| Subspaces | | |
+| Span | | |
+| Linear independence | | |
+| Basis | | |
+| Dimension | | |
+| Null space | | |
+| Column space | | |
+| Rank | | |
+
+### Eigenvalues & Decompositions
+| Topic | Level (0-4) | Notes |
+|-------|-------------|-------|
+| Eigenvalues | | |
+| Eigenvectors | | |
+| Characteristic polynomial | | |
+| Diagonalization | | |
+| LU decomposition | | |
+| QR decomposition | | |
+| SVD | | |
+| Orthogonalization (Gram-Schmidt) | | |
+
+### Applications
+| Topic | Level (0-4) | Notes |
+|-------|-------------|-------|
+| Linear regression | | |
+| PCA | | |
+| Graphics transformations | | |
+| Least squares | | |
+| Optimization | | |
+
+---
+
+## Part 2: Computational Problems
+
+### Problem 1: Vector Operations (Beginner)
+Given vectors u = [2, -1, 3] and v = [1, 4, -2]:
+
+a) Compute u + v
+b) Compute 3u - 2v  
+c) Compute ||u|| (magnitude)
+d) Compute u · v (dot product)
+e) Are u and v orthogonal?
+
+**Can you solve this?** ☐ Yes ☐ No ☐ Partially
+
+---
+
+### Problem 2: Matrix Multiplication (Beginner)
+Compute AB where:
+```
+A = [1  2]    B = [5  6]
+    [3  4]        [7  8]
+```
+
+**Can you solve this?** ☐ Yes ☐ No ☐ With formula
+
+---
+
+### Problem 3: Solve Linear System (Intermediate)
+Solve using Gaussian elimination:
+```
+ x + 2y - z = 3
+2x - y + z = 1
+3x + y + 2z = 11
+```
+
+**Can you solve this?** ☐ Yes ☐ No ☐ With steps
+
+---
+
+### Problem 4: Matrix Inverse (Intermediate)
+Find the inverse of:
+```
+A = [2  1]
+    [5  3]
+```
+
+**Can you solve this?** ☐ Yes ☐ No ☐ With formula
+
+---
+
+### Problem 5: Eigenvalues (Advanced)
+Find eigenvalues and eigenvectors of:
+```
+A = [3  1]
+    [1  3]
+```
+
+**Can you solve this?** ☐ Yes ☐ No ☐ With steps
+
+---
+
+### Problem 6: Application - Linear Regression (Advanced)
+Given data points: (1,2), (2,4), (3,5), (4,6)
+
+Set up and solve the least squares problem to find the best-fit line y = mx + b using matrix methods.
+
+**Can you solve this?** ☐ Yes ☐ No ☐ Know concept only
+
+---
+
+## Part 3: Knowledge Gap Analysis
+
+### Based on Self-Assessment
+
+**Count your scores:**
+- Topics at Level 0: ___
+- Topics at Level 1: ___
+- Topics at Level 2: ___
+- Topics at Level 3: ___
+- Topics at Level 4: ___
+
+**Total topics:** ___
+
+### Based on Problems
+
+**Problems solved:**
+- Problem 1 (Vectors): ☐
+- Problem 2 (Matrix Mult): ☐
+- Problem 3 (Systems): ☐
+- Problem 4 (Inverse): ☐
+- Problem 5 (Eigenvalues): ☐
+- Problem 6 (Application): ☐
+
+**Total solved:** ___ / 6
+
+---
+
+## 📊 Proficiency Level Determination
+
+### Absolute Beginner (0-20% Level 2+, 0-1 problems)
+- **Start:** Phase 1 from Module 1.1
+- **Timeline:** 10-12 months to applications
+- **Focus:** Build from scratch, emphasize geometric intuition
+- **Resources:** 3Blue1Brown, Khan Academy, "Linear Algebra Done Right"
+
+### Beginner (20-40% Level 2+, 1-2 problems)
+- **Start:** Phase 1 with quick review, focus on Phase 2
+- **Timeline:** 8-10 months to applications
+- **Focus:** Strengthen basics, master systems and inverses
+- **Resources:** Gilbert Strang lectures, "Linear Algebra and Its Applications"
+
+### Intermediate (40-60% Level 2+, 3-4 problems)
+- **Start:** Phase 2, review Phase 1 as needed
+- **Timeline:** 6-8 months to applications
+- **Focus:** Vector spaces, eigenvalues, decompositions
+- **Resources:** Strang's book, MIT OCW
+
+### Advanced (60-80% Level 2+, 5 problems)
+- **Start:** Phase 3, skim Phase 1-2
+- **Timeline:** 4-6 months to specialization
+- **Focus:** Advanced theory and applications
+- **Resources:** "Matrix Analysis", research papers
+
+### Expert (80%+ Level 3+, 6 problems)
+- **Start:** Phase 4-5 (Applications & Specialization)
+- **Timeline:** 2-4 months to deep specialization
+- **Focus:** Specialized applications, cutting-edge topics
+- **Resources:** Research papers, advanced texts
+
+---
+
+## 🎯 Personalized Learning Path
+
+### Your Starting Point
+**Based on assessment:** _______________ 
+
+### Recommended Phase
+**Start at Phase:** _______________
+
+### Topics to Review First
+1. _______________
+2. _______________
+3. _______________
+
+### Topics to Skip (Already Mastered)
+1. _______________
+2. _______________
+
+### Weak Areas to Focus On
+1. _______________
+2. _______________
+
+### Estimated Timeline to Advanced
+**From your starting point:** ___ months
+
+---
+
+## 📝 Action Items
+
+### Immediate (This Week)
+1. ☐ Complete this assessment
+2. ☐ Set up Python + NumPy or MATLAB
+3. ☐ Watch 3Blue1Brown: "Essence of Linear Algebra" (video 1)
+4. ☐ Review recommended phase in Master Plan
+5. ☐ Join math communities (r/learnmath, Math Stack Exchange)
+
+### First Month
+1. ☐ Complete ____ modules
+2. ☐ Solve 100+ practice problems
+3. ☐ Watch all 3Blue1Brown videos (11 total)
+4. ☐ Implement basic operations in code
+5. ☐ Take first monthly exam
+
+---
+
+## 🔄 Reassessment Schedule
+
+- **Week 4:** Quick progress check
+- **Month 3:** Comprehensive reassessment
+- **Month 6:** Mid-journey assessment
+- **Month 9:** Full reassessment
+- **Month 12:** Expert level check
+
+---
+
+## 📚 Additional Resources
+
+### Video Series
+- **3Blue1Brown:** "Essence of Linear Algebra" (MUST WATCH)
+- **MIT OCW:** Gilbert Strang's 18.06
+- **Khan Academy:** Linear Algebra playlist
+
+### Interactive Tools
+- **GeoGebra:** Visualize vectors and transformations
+- **WolframAlpha:** Compute anything
+- **MATLAB/Octave:** Numerical experiments
+- **Python + NumPy:** Programming practice
+
+### Problem Sources
+- MIT OCW problem sets
+- Gilbert Strang's textbook exercises
+- Linear Algebra Done Right exercises
+- Math Stack Exchange
+
+---
+
+**Date Completed:** _______________
+**Next Reassessment:** _______________
+**Notes:**
+_______________________________________________
+_______________________________________________
+
--- a/learning_plans/linear_algebra/README.md
+++ b/learning_plans/linear_algebra/README.md
@@ -0,0 +1,378 @@
+# Linear Algebra Learning Plan
+
+## 📐 Welcome to Your Linear Algebra Mastery Journey!
+
+This comprehensive learning plan will guide you from basic vectors to advanced applications in machine learning, computer graphics, and data science.
+
+---
+
+## 📚 What's Included
+
+### 1. Master Plan (`00_LINEAR_ALGEBRA_MASTER_PLAN.md`)
+Your complete roadmap containing:
+- **22 detailed modules** organized in 5 phases
+- **From geometric intuition to abstract theory**
+- **Applications in ML, graphics, data science**
+- **Resource recommendations** (textbooks, videos, tools)
+- **Milestone achievements** with project ideas
+- **Specialization paths** (ML, Graphics, Quantum, Computational)
+
+### 2. Knowledge Graph (`01_KNOWLEDGE_GRAPH.md`)
+Complete dependency map showing:
+- **15 knowledge levels** from basics to expert
+- **Topic dependencies** clearly mapped
+- **Parallel learning opportunities**
+- **Visual knowledge tree**
+- **Critical learning path**
+
+### 3. Initial Assessment (`02_INITIAL_ASSESSMENT.md`)
+Determine your starting point with:
+- **Self-assessment** covering 40+ topics
+- **6 computational problems** (beginner to expert)
+- **Proficiency level determination**
+- **Personalized recommendations**
+
+### 4. Assessments Directory (`assessments/`)
+Track your exam performance:
+- **Personalized assessments** after each exam
+- **Strengths and weaknesses** identified
+- **Progress tracking** over time
+
+---
+
+## 🎯 Learning Path Overview
+
+### Phase 1: Foundations (1.5-2 months)
+**Goal:** Master vectors and matrices
+- Module 1.1: Vectors Basics (geometric)
+- Module 1.2: Dot Product & Vector Operations
+- Module 1.3: Matrices Basics
+- Module 1.4: Matrix Properties
+
+### Phase 2: Core Theory (2-3 months)
+**Goal:** Master systems, decompositions, eigenvalues
+- Module 2.1: Systems of Linear Equations
+- Module 2.2: Matrix Inverses
+- Module 2.3: Determinants
+- Module 2.4: Vector Spaces
+- Module 2.5: Linear Transformations
+- Module 2.6: Eigenvalues & Eigenvectors
+
+### Phase 3: Advanced Topics (1.5-2 months)
+**Goal:** Master orthogonality and decompositions
+- Module 3.1: Orthogonality
+- Module 3.2: Inner Product Spaces
+- Module 3.3: Matrix Decompositions (LU, QR, SVD)
+- Module 3.4: Norms & Conditioning
+
+### Phase 4: Applications (1-2 months)
+**Goal:** Apply to real-world problems
+- Module 4.1: Machine Learning (PCA, regression)
+- Module 4.2: Computer Graphics (transformations)
+- Module 4.3: Optimization
+- Module 4.4: Data Science
+
+### Phase 5: Specialization (Ongoing)
+**Choose your path:**
+- Machine Learning Deep Dive
+- Computational Linear Algebra
+- Quantum Computing
+- Advanced Applications
+
+---
+
+## 🚀 Quick Start
+
+### Step 1: Prerequisites (Optional, 1-2 days)
+- Review basic algebra if rusty
+- Set up Python + NumPy OR MATLAB
+- Test with simple calculations
+
+### Step 2: Assessment (1-2 hours)
+1. Open `02_INITIAL_ASSESSMENT.md`
+2. Complete self-assessment
+3. Try computational problems
+4. Determine your level
+
+### Step 3: Build Intuition (1 week)
+1. **WATCH:** 3Blue1Brown "Essence of Linear Algebra" (11 videos, ~3 hours total)
+2. This series provides incredible geometric intuition
+3. Watch before heavy studying!
+
+### Step 4: Study (Daily)
+1. Read theory (30-40 min)
+2. Solve problems (30-40 min)
+3. Prove theorems (20-30 min)
+4. Code implementations (optional)
+
+---
+
+## 💻 Recommended Tools
+
+### Python + NumPy (Recommended for Programmers)
+```python
+import numpy as np
+
+# Vectors
+v = np.array([1, 2, 3])
+w = np.array([4, 5, 6])
+dot = np.dot(v, w)          # Dot product
+norm = np.linalg.norm(v)    # Magnitude
+
+# Matrices
+A = np.array([[1, 2], [3, 4]])
+B = np.linalg.inv(A)        # Inverse
+det = np.linalg.det(A)      # Determinant
+eig = np.linalg.eig(A)      # Eigenvalues
+
+# Solve systems
+x = np.linalg.solve(A, b)   # Solve Ax = b
+
+# Decompositions
+U, S, Vt = np.linalg.svd(A) # SVD
+Q, R = np.linalg.qr(A)      # QR
+```
+
+### MATLAB/Octave (Industry Standard)
+```matlab
+% Matrices are first-class citizens
+A = [1 2; 3 4];
+B = inv(A);              % Inverse
+det_A = det(A);          % Determinant
+[V, D] = eig(A);         % Eigenvalues
+
+% Solve systems
+x = A \ b;               % Solve Ax = b
+
+% Decompositions
+[U, S, V] = svd(A);      % SVD
+[Q, R] = qr(A);          % QR
+```
+
+---
+
+## 📚 Essential Resources
+
+### Must-Watch Videos
+1. **3Blue1Brown: "Essence of Linear Algebra"** (11 videos)
+   - BEST visual intuition
+   - Watch FIRST before anything else
+   - Free on YouTube
+
+### Textbooks (In Order)
+1. **"Introduction to Linear Algebra"** by Gilbert Strang
+   - Best overall introduction
+   - Clear explanations
+   - Many applications
+   
+2. **"Linear Algebra and Its Applications"** by David Lay
+   - Very accessible
+   - Application-focused
+   - Great for beginners
+
+3. **"Linear Algebra Done Right"** by Sheldon Axler
+   - More theoretical
+   - Avoids determinants initially
+   - Beautiful proofs
+
+4. **"Matrix Analysis"** by Horn & Johnson
+   - Advanced reference
+   - Comprehensive
+   - For deep study
+
+### Online Courses
+- **MIT OCW:** Gilbert Strang's 18.06 (legendary!)
+- **Khan Academy:** Linear Algebra series
+- **Brilliant.org:** Interactive problems
+
+---
+
+## 🏆 Key Milestones
+
+### Milestone 1: Vector & Matrix Fluency ✅
+- **Timing:** Month 2
+- **Skills:** All vector/matrix operations
+- **Project:** Vector/matrix library in Python
+- **Test:** Solve 20 problems in 30 minutes
+
+### Milestone 2: Systems Mastery ✅
+- **Timing:** Month 4-5
+- **Skills:** Solve any linear system, compute inverses
+- **Project:** Linear equation solver
+- **Test:** Pass comprehensive exam (75%+)
+
+### Milestone 3: Eigenvalue Mastery ✅
+- **Timing:** Month 6-7
+- **Skills:** Eigenvalues, eigenvectors, diagonalization
+- **Project:** Markov chain simulator
+- **Test:** Pass advanced exam (70%+)
+
+### Milestone 4: SVD & Applications ✅
+- **Timing:** Month 8-9
+- **Skills:** SVD, PCA, graphics transforms
+- **Project:** Image compression or PCA implementation
+- **Test:** Apply to real data
+
+### Milestone 5: Specialization ✅
+- **Timing:** Month 10+
+- **Skills:** Deep expertise in chosen area
+- **Project:** ML model, graphics engine, or quantum algorithm
+- **Certification:** Professional portfolio
+
+---
+
+## 💡 Linear Algebra Learning Tips
+
+### Do's ✅
+- **Visualize everything** - Draw vectors and transformations
+- **Use 3Blue1Brown** - Best intuition builder
+- **Solve many problems** - Fluency requires practice
+- **Implement in code** - Programming solidifies understanding
+- **Prove key theorems** - Understand WHY, not just HOW
+- **Connect to applications** - See real-world relevance
+- **Start geometric** - Intuition before abstraction
+
+### Don'ts ❌
+- Don't memorize formulas without understanding
+- Don't skip geometric interpretation
+- Don't avoid proofs entirely
+- Don't neglect computational practice
+- Don't rush through fundamentals
+- Don't study in isolation (use visualizations)
+
+---
+
+## 🎯 Why Learn Linear Algebra?
+
+### Foundation for Modern Tech
+- **Machine Learning:** PCA, neural networks, optimization
+- **Computer Graphics:** ALL transformations are matrices
+- **Data Science:** Dimensionality reduction, analysis
+- **Quantum Computing:** Quantum states are vectors
+- **Computer Vision:** Image processing, feature extraction
+- **Natural Language Processing:** Word embeddings, transformers
+
+### Real Applications
+- Netflix recommendations (SVD, matrix factorization)
+- Google PageRank (eigenvectors of web graph)
+- Face recognition (eigenfaces, PCA)
+- 3D video games (transformation matrices)
+- Self-driving cars (sensor fusion, optimization)
+- ChatGPT/LLMs (attention is matrix operations!)
+
+### Career Impact
+- Required for ML engineer roles
+- Essential for data science
+- Critical for graphics programming
+- Foundation for AI research
+- Needed for quantitative finance
+
+---
+
+## 📊 Study Schedules
+
+### Full-Time (3-4 hours/day)
+- **Timeline:** 5-6 months to applications
+- **Daily:** 1 hour theory + 1-2 hours problems + 1 hour coding
+- **Projects:** 1-2 per week
+- **Pace:** 1 module per week
+
+### Part-Time (1.5-2 hours/day)
+- **Timeline:** 8-10 months to applications
+- **Daily:** 40 min theory + 40 min problems + 20 min review
+- **Projects:** 1 per week
+- **Pace:** 1 module per 1.5-2 weeks
+
+### Casual (1 hour/day)
+- **Timeline:** 12-15 months to applications
+- **Daily:** 30 min theory + 30 min problems
+- **Projects:** 2 per month
+- **Pace:** 1 module per 2-3 weeks
+
+---
+
+## 🎓 Integration with Tech Learning
+
+### Python Integration
+Use NumPy to implement all concepts:
+- Vectors and matrices
+- Linear transformations
+- Eigenvalue computation
+- SVD and PCA
+- ML applications
+
+### C++ Integration
+Implement for performance:
+- Matrix libraries
+- Graphics transformations
+- Game engine math
+- Scientific computing
+
+### Machine Learning
+Linear algebra is EVERYWHERE:
+- Data representation
+- Model parameters
+- Forward/backward pass
+- Optimization
+- Dimensionality reduction
+
+---
+
+## 🌟 What Makes This Plan Special
+
+### Visual & Intuitive
+- Emphasizes geometric understanding
+- 3Blue1Brown integration
+- Visualization tools
+- Draw everything!
+
+### Computation & Theory Balanced
+- 60% computational practice
+- 25% theoretical understanding
+- 15% applications
+- Learn by doing AND understanding
+
+### Application-Driven
+- See real uses immediately
+- Build actual projects
+- Connect to ML, graphics, data science
+- Not just abstract math
+
+### Modern & Practical
+- Python/NumPy focus
+- Industry-relevant skills
+- Modern applications (ML, AI)
+- Cutting-edge topics
+
+---
+
+## 🎯 Your Next Steps
+
+1. ☐ Read this README
+2. ☐ **WATCH:** 3Blue1Brown videos 1-3 (build intuition!)
+3. ☐ Complete `02_INITIAL_ASSESSMENT.md`
+4. ☐ Review `00_LINEAR_ALGEBRA_MASTER_PLAN.md`
+5. ☐ Check `01_KNOWLEDGE_GRAPH.md` for dependencies
+6. ☐ Set up NumPy or MATLAB
+7. ☐ Start Module 1.1!
+
+---
+
+## 🌟 Inspiration
+
+*"Linear algebra is the mathematics of data."*
+— Gilbert Strang
+
+*"You can't do machine learning without linear algebra."*
+— Every ML engineer
+
+*"The more I learn about linear algebra, the more I realize it's everywhere."*
+— You, after completing this course!
+
+---
+
+**Linear algebra is the foundation of modern technology. Master it and unlock AI, graphics, data science, and more! 📐🚀**
+
+**Last Updated:** October 21, 2025
+**Status:** ✅ Complete learning plan
+**Next Review:** January 2026
--- a/learning_plans/linear_algebra/assessments/README.md
+++ b/learning_plans/linear_algebra/assessments/README.md
@@ -0,0 +1,81 @@
+# Linear Algebra Assessments Directory
+
+## 📁 Purpose
+
+This directory contains all your personalized Linear Algebra exam assessments and performance reviews.
+
+---
+
+## 📊 What's Stored Here
+
+### Exam Result Assessments
+- Detailed analysis of your exam performance
+- Problem-by-problem breakdown
+- Strengths and weaknesses identified
+- Personalized study recommendations
+- Progress tracking over time
+
+### Assessment Format
+**Filename:** `howard_linear_algebra_{exam_id}_assessment.md`
+**Example:** `howard_linear_algebra_basics_v1_assessment.md`
+
+---
+
+## 📝 Future Assessments
+
+As you take Linear Algebra exams, this folder will contain:
+- Foundations exam assessments
+- Core theory exam assessments
+- Advanced topics exam assessments
+- Applications exam assessments
+- Retake assessments showing improvement
+
+---
+
+## 🎯 How to Use These Assessments
+
+### After Each Exam
+1. Review the assessment file
+2. Identify your strengths (celebrate!)
+3. Note areas for improvement
+4. Follow the recommended study plan
+5. Track progress over time
+
+### For Progress Tracking
+- Compare assessments over time
+- See improvement in weak areas
+- Verify mastery before advancing
+- Celebrate milestones
+
+### For Study Planning
+- Use weakness identification for focused study
+- Follow recommended action plans
+- Prioritize high-impact topics
+- Optimize learning time
+
+---
+
+## 🔗 Integration with Learning Plan
+
+Assessments directly reference:
+- **Master Plan:** `/learning_plans/linear_algebra/00_LINEAR_ALGEBRA_MASTER_PLAN.md`
+- **Knowledge Graph:** `/learning_plans/linear_algebra/01_KNOWLEDGE_GRAPH.md`
+- **Initial Assessment:** `/learning_plans/linear_algebra/02_INITIAL_ASSESSMENT.md`
+
+---
+
+## 📊 Expected Contents Over Time
+
+```
+assessments/
+├── README.md (this file)
+├── howard_linear_algebra_foundations_v1_assessment.md (future)
+├── howard_linear_algebra_intermediate_v1_assessment.md (future)
+├── howard_linear_algebra_eigenvalues_v1_assessment.md (future)
+├── howard_linear_algebra_applications_v1_assessment.md (future)
+└── progress_summary.md (coming soon)
+```
+
+---
+
+**Keep all your Linear Algebra assessments here for comprehensive progress tracking!** 📐✨