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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.
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