- standard aand abstract scalar product, orthogonal basis, Gram-Schmidt orthogonalization,

- ortogonal and unitary mappings and matrices, rotations (especially in 3D), group properties,

- vlastní čísla a vlastní vektory, diagonalizovatelné operátory, Jordanův kanonický tvar,

- unitary and orthogonal diagonalization, spectral theorems, singular value decomposition,

- bilinear and quadratic forms, their matrix, orthogonalization, inertia theorem,

- afine spaces, afine and metric classification of quadratic forms

The second introductory lecture in linear algebra for General Mathematics, Financial Mathematics, and Information

Security