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.
- 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)
- 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 (updated with an example)
- Diagonalization
Similar matrices, diagonalization, Jordan normal form (21:48, 408M)
- slides only (added proof of the Jordan normal form theorem), smaller version (54M)
Special complex matrices, diagonalization of a Hermitian matrix (19:25, 287M)
- slides only, smaller version (33M)
May 9, 2022: Fixed the example of orthogonal matrix on page 1.
- 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)
May 3, 2022: updated presentation - proof of the theorem about diagonalization of q. forms is rewritten so that the transposed matrix is on the left
Conics and quadrics (6:19, 11M)
- slides only, smaller version (5M)
- 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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