Videos and examples from lectures LA II

Video lectures

The audio is sometimes not synced well, sorry. I plan to fix it with the next retake.
  1. Determinants
    Determinants, Laplace expansion, adjoint matrix, Cramer's rule (56:38, 829M) - slides only, smaller version (114M)
    The number of spanning trees of a graph (23:43, 240M) - slides only, smaller version (39M)
  2. Polynomials
    Polynomials, Vandermonde matrix, Lagrange interpolation (28:50, 502M) - slides only, smaller version (62M)
  3. Eigenvalues and eigenvectors
    Eigenvalues and eigenvectors of linear maps and matrices, characteristic polynomial (32:52, 887M) - slides only, smaller version (97M)
    Homogeneous systems of first order linear differential equations with constant coefficients (4:35, 8M) - slides only
    Cayley-Hamilton theorem (8:09, 14M) - slides only
  4. Diagonalization
    Similar matrices, diagonalization, Jordan normal form (21:48, 408M) - slides only, smaller version (54M)
    Special complex matrices, diagonalization of a Hermitian matrix (19:25, 291M) - slides only, smaller version (39M)
  5. Inner spaces
    Inner product, norm, Cauchy-Schwarz inequality (20:39, 421M) - slides only, smaller version (25M) (updated, fixed terminology GM -> RMS)
    Orthogonality, orthonormal bases, Fourier coefficients (26:11, 777M) - slides only, smaller version (72M)
    Orthogonal projection, Gram-Schmidt orthonormalization, isometry, orthogonal complement (43:53, 719M) - slides only, smaller version (93M)
  6. Positive definite matrices
    Positive definite matrices, Cholesky factorization, Sylvester's condition (33:58, 634M) - slides only, smaller version (78M)
  7. Bilinear and quadratic forms
    Bilinear and quadratic forms, their matrices, Sylvester's law of inertia (43:38, 672M) - slides only, smaller version (93M)
  8. Applications
    The number of even subgraphs of a graph (10:27, 194M) - slides only, smaller version (18M)
    The maximum number of lines spanning the same angle (9:07, 191M) - slides only, smaller version (17M)
(The small versions may have sound problems on some devices.)

Examples