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Linear Algebra for Machine Learning

Introduction​

This comprehensive linear algebra course is structured around Gilbert Strang's "Introduction to Linear Algebra" and is specifically designed for machine learning practitioners. The material is organized into four major sections, each covering fundamental and advanced topics.

Course Structure​

The course is divided into 4 sections, each containing:

  1. High-level Overview - Conceptual understanding with intuition
  2. Mathematical Deep-dive - Rigorous proofs and theorems
  3. Problems - University-level exam questions
  4. Python Implementation - Computational examples and code

The Four Sections​

Section 1: Core Linear System Theory​

Focus on fundamental algebraic structures and solution spaces.

Topics:

  • Vector spaces and subspaces
  • Linear independence, basis, and dimension
  • The Four Fundamental Subspaces
  • Linear transformations
  • Matrix multiplication and LU decomposition

Section 2: Spectral Theory & Matrix Decompositions​

Focus on eigenvalue analysis and matrix factorizations.

Topics:

  • Eigenvalues and eigenvectors
  • Diagonalization and powers of matrices
  • Matrix exponentials and differential equations
  • Singular Value Decomposition (SVD)
  • Positive definite matrices

Section 3: Geometric & Optimization Methods​

Focus on orthogonality, projections, and optimization.

Topics:

  • Orthogonal vectors and subspaces
  • Projections and least squares
  • Gram-Schmidt process
  • Optimization: minima, maxima, and saddle points
  • Finite Element Method

Section 4: Computational Methods & Applications​

Focus on numerical algorithms and advanced applications.

Topics:

  • Matrix norms and condition numbers
  • Eigenvalue computation algorithms
  • Iterative methods for solving linear systems
  • Linear programming and the Simplex Method
  • Network models and game theory