Outline:

1. Canonical forms: Jordan and rational forms, Schur form, polar and singular value decompositions, LU, QR and Cholesky factorizations.
2. Hermitian matrices: characterization of eigenvalues, Weyl's theorem, Sylvester law of inertia, Courant-Fischer min-max theorem, Cauchy interlacing theorem, Conjugate gradient method, Krylov space.
3. Special matrices: normal, nonnegative, stochastic, stable matrices.

Objective:

The course provides the students with the knowledge of the matrix theory.

Textbook:

1. Roger A. Horn and Charles R. Johnson, Matrix Analysis, Cambridge University Press, 1990