## Тематический план

• ### Lecture 1

Background in Linear Algebra. Basic definitions. Types and structures of square matrices.

• ### Lectures 2 and 3

Vector and matrix norms. Range and kernel. Orthonormal vectors. Gram-Schmidt process. Eigenvalues and their multiplicities. Basic matrix factorizations and canonical forms: QR, diagonal form, Jordan form, Schur form. Basic matrix factorizations: SVD, LU, Cholessky. Existence of solution. Perturbation analysis and condition number. Errors and costs.