MAT 357 - Linear Algebra III

Course Objectives

To give knowledge about the following subjects:
Polynomials, Polynomial matrices, matrix functions, canonical forms.

Course Description

Polynomials; polynomial rings, prime factorization, Lagrange interpolation. Canonical forms; characteristic polynomial, minimal polynomial, eigen-spaces, invariant subspaces, diagonalization, triangulation, invariant direct summation, separation theorem. Rational and Jordan form; kernel subspaces, cyclic subspaces, Jordan forms, finding invariant factors. Bilinear forms; bilinear forms, symmetric forms, unitary and orthogonal transformations, conjugate spaces.