Linear Algebra

Elimination, eigenvalues and the SVD — with the geometry kept in view.

Syllabus

  1. Vectors, Elimination & Subspaces

    1. Vectors, Linear Combinations & the Geometry of Rⁿ
    2. Systems of Equations & Gaussian Elimination
    3. Matrix Algebra, Inverses & the LU Factorization
    4. Vector Spaces, Subspaces & the Four Fundamental Subspaces
    5. Independence, Basis, Dimension & Rank

  2. Bases, Orthogonality & Least Squares

    1. Linear Transformations & Change of Basis
    2. Orthogonality, Projections & Gram-Schmidt
    3. Least Squares & Data Fitting

  3. Determinants, Eigenvalues & Spectral Theory

    1. Determinants
    2. Eigenvalues & Diagonalization
    3. Symmetric Matrices, Spectral Theorem & Quadratic Forms

  4. SVD, Markov Chains & PCA

    1. The Singular Value Decomposition
    2. Markov Matrices, PageRank & the Matrix Exponential
    3. Principal Component Analysis & Course Capstone