Videos and presentations from lectures LA 2

In comparison with videos, presentations may have some inaccuracies fixed and may include further information (examples, images).

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 (54:10, 464M) - slides only, smaller version (78M)
   The number of spanning trees of a graph (23:50, 65M) - slides only, smaller version (27M)
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 (updated with an example)
4. Diagonalization
   Similar matrices, diagonalization (21:48, 408M) - slides only (the presentation on the Jordan normal form was separated), smaller version (54M)
   Special complex matrices, diagonalization of a Hermitian matrix (19:25, 287M) - slides only, smaller version (33M)
   Jordan normal form (part of the explanation recorded in the video on similar matrices)
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)
   Conics and quadrics (6:19, 11M) - slides only, smaller version (5M)
8. Applications
   The maximum number of lines spanning the same angle (9:07, 191M) - slides only, smaller version (17M)

See also videos from the winter term.

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