Linear Algebra
Two full courses at UofT (MATA22, MATB24) — from matrix arithmetic through abstract linear maps over arbitrary fields.
Courses: Linear Algebra I (MATA22), Linear Algebra II (MATB24 — proof-based, abstract)
Topics covered
- Vector spaces, subspaces, bases, dimension
- Linear transformations and matrix representations
- Eigenvalues, eigenvectors, diagonalisation, spectral theorem
- Inner product spaces, orthogonality, Gram-Schmidt process
- Jordan canonical form, minimal polynomials
- Singular value decomposition (SVD)
Why it matters
Linear algebra is the language of ML: neural networks are compositions of linear maps with non-linearities; SVD underlies dimensionality reduction (PCA); NumPy and SciPy expose these operations directly. It’s also the mathematical backbone of Quantum Mechanics (Hilbert spaces, operators).
Related: Mathematics, ML, NumPy, Physics, Quantum Mechanics