Aktuálně tento předmět nevyučuji.

1. Dot product, inner product. Cauchy-Schwarz inequality.
2. Norm and orthogonality. Orthonormal basis, Gram-Schmidt orthogonalization.
3. Othogonal complement and projection.
4. Method of least squares, pseudoinverse. Isometries and orthogonal matrices.
5. Determinants - definition, row operations.
6. Determinants - multiplicativity, linear equations, inverse.
7. Applications of determinants. Eigenvalues and eigenvectors.
8. Matrix similarity. Diagonalization and Jordan normal form.
9. Cayley-Hamilton theorem. Symmetric and positive matrices, Perron-Frobenius theorem.
10. Bilinear and quadratic forms. Classification of quadrics.
11. Positive (semi)definiteness.
12. Matrix decompositions.