2- Course Aim :-

The Topics of this course include: Characteristic and minimal polynomial. Eigenvalues, field of values. Similarity transformations: Diagonalization and Jordan forms over arbitrary fields. Schur form and spectral theorem for normal matrices. Quadratic forms and Hermitian matrices: variational characterization of the eigenvalues, inertia theorems. Singular value decomposition, generalized inverse, projections, and applications.  Positive matrices, Perron-Frobenius theorem. Markov chains and stochastic matrices. M-matrices. Structured matrices (Toeplitz, Hankel, Hessenberg). Matrices and optimization (e.g., linear complementarity problem, conjugate gradient). Other topics and applications depending on the interest of the instructor.