EE635:APPLIED LINEAR ALGEBRA IN ELECTRICAL ENGINEERING
Vector spaces, linear dependence, basis; Representation of linear transformations with respect to a basis.;Inner product spaces, Hilbert spaces, linear functions; Riesz representation theorem and adjoints.;Orthogonal projections, products of projections, orthogonal direct sums; Unitary and orthogonal transformations, complete orthonormal sets and Parseval's identity; Closed subspaces and the projection theorem for Hilbert spaces.;Polynomials: The algebra of polynomials, matrix polynomials, annihilating polynomials and invariant subspaces, forms.;Applications: Complementary orthogonal spaces in networks, properties of graphs and their relation to vector space properties of their matrix representations; Solution of state equations in linear system theory; Relation between the rational and Jordan forms.;Numerical linear algebra: Direct and iterative methods of solutions of linear equations; Matrices, norms, complete metric spaces and complete normal linear spaces (Banach spaces); Least squares problems (constrained and unconstrained); Eigenvalue problem.
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E.Kreyszig, ntroductory functional analysis with applications John Wiley, 1978.