Commit e6997af
committed
Add comprehensive linear algebra topics to module
Added extensive coverage of advanced linear algebra topics:
1. Solving Systems of Linear Equations
- Gaussian elimination and row reduction
- Solving Ax = 0 (homogeneous systems)
- Solving Ax = b (non-homogeneous systems)
- Pivot variables and free variables
2. Column Space and Nullspace
- Column space (range) computation
- Nullspace (kernel) computation
- Rank-nullity theorem
3. The Four Fundamental Subspaces
- Column space, row space, nullspace, left nullspace
- Orthogonality relationships
- Complete subspace analysis
4. Determinants
- Properties and computation
- Cofactor expansion
- Cramer's rule for solving systems
5. Diagonalization
- Conditions for diagonalizability
- Computing powers of matrices
- Applications in ML
6. Matrix Exponentials
- Definition and computation
- Solving differential equations
- Applications in continuous-time systems
7. Pseudoinverse (Moore-Penrose)
- SVD-based computation
- Left and right inverses
- Applications in least squares
8. Positive Definite Matrices
- Properties and checking
- Cholesky decomposition
- Applications in ML (covariance, kernels)
9. Complex Matrices and FFT
- Hermitian and unitary matrices
- Fast Fourier Transform
- Applications in signal processing and CNNs
All topics include ML-focused explanations, Python code examples, and practical applications. Updated table of contents with all new sections.1 parent 7897da0 commit e6997af
1 file changed
+967
-0
lines changed
0 commit comments