Тематический план

• Module 1. Lecture 1

Lecture 1. Background in Linear Algebra. Basic definitions. Types and structures of square matrices.

• Lectures 2-5

Lecture 2 Vector and matrix norms. Range and kernel. Existence of Solution. Orthonormal vectors.

Lecture 3. Gram-Schmidt process. Eigenvalues and their multiplicities. Basic matrix factorizations and canonical forms: QR, diagonal form, Jordan form, Schur form.

Lecture 4. Basic matrix factorizations: SVD, LU, Cholessky. Properties of normal, Hermittian matrices and positive definite matrices.

Lecture 5. Perturbation analysis and condition number. Errors and costs.