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1 Inner product on complex vector spaces, properties of hermitian, unitary matrices,
2 generalized eigenvectors, vector and matrix norms,
3 Basic Matlab terms and matlab codes related to the matrix computations.
4 The definition of matrix polynomials and elementary operations of matrix polynomials,
5 Equivalence, annihilating, characteristic and minimal polynomials, invariant polynomials,
6 Smith canonical form, similarity and the first normal form,
7 Elementary divisors, the second normal form,
8 Jordan canonical form and problem solutions,
9 Matrix Functions; Lagrange and Hermite interpolatory polynomials,
10 Definition of a function of a matrix and properties of functions of matrices,
11 Spectral resolution of f(A),
12 Calculation of e^At and the inverse of (sI-A), in terms of component matrices of A,
13 Solutions of the system of differantial equations,
14 Solutions of the system of differantial equations, |