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.
- 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)
- Polynomials
Polynomials, Vandermonde matrix, Lagrange interpolation (28:50, 502M)
- slides only, smaller version (62M)
- 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
- 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)
- 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)
- Positive definite matrices
Positive definite matrices, Cholesky factorization, Sylvester's condition (33:58, 634M)
- slides only, smaller version (78M)
- Bilinear and quadratic forms
Bilinear and quadratic forms, their matrices, Sylvester's law of inertia (43:38, 672M)
- slides only, smaller version (93M)
- 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