MAT 339E - Matrix Theory and Applications

Course Objectives

1-To give ability about coding and calculation of the matrices in MATLAB.
2-To teach the general knowledge about the matrix polynomials,
3-To teach the general knowledge about the matrix functions,
4-To give ability about the analytical calculation of the matrix functions, especially the matrices e^At and (sI-A)^-1,
5-To give ability to solve the system of differential equations in terms of matrix functions.

Course Description

Inner product on complex vector spaces, hermitian, unitary matrices, generalized eigenvectors, vector and matrix norms, computations in matlab. Matrix Polynomials; Elementary operations for matrix polynomials, equivalence, annihilating, characteristic, minimal and invariant polynomials. Normal Forms; the Smith canonical form, similarity, the first normal form, elementary divisors, the second normal form and Jordan canonical form. Functions of Matrices; Lagrange and Hermite interpolatory polynomials, definitions, properties and spectral solutions of functions of matrices, solutions of the system of differantial equations by matrix fuctions.