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Weights in neural networks are stored as large matrices; optimization relies heavily on gradients and vector calculus.
| Part | Chapters | Core Themes | |------|----------|-------------| | | 1‑4 | Vector spaces, subspaces, linear independence, bases, dimension | | Part II: Linear Transformations | 5‑8 | Matrix representation, kernel & image, rank‑nullity theorem | | Part III: Systems of Linear Equations | 9‑11 | Gaussian elimination, LU decomposition, consistency criteria | | Part IV: Eigen Theory | 12‑15 | Eigenvalues, eigenvectors, diagonalization, applications | | Part V: Advanced Topics | 16‑18 | Inner product spaces, orthogonal projections, Gram‑Schmidt, spectral theorem |