Spectral perturbation theory for matrices and matrix pencils

Code: MA733 | L-T-P-C: 4-0-0-8

MA733 Spectral perturbation theory for matrices and matrix pencils L-T-P-C [4-0-0-8]

Prerequisites: Nil

Matrix valued analytic functions, projections. Invariant subspaces and spectral decompositions, singular value decompositions, pairs of projections. Matrix norms, unitarily invariant norms, gap between subspaces. General perturbation theory for matrices, Bauer-Fike and Henrici theorems, Hoffman-Wielandt theorem, analytic perturbation theory for eigenvalues. Invariant subspaces, Sylvester operator, perturbation of spectral subspaces. Matrix pencils, eigenvalues and eigenvectors of regular pencils, triangular and Weierstrass forms, Kronecker canonical form, deflating subspaces, definite pencils, perturbation of eigenvalues of regular pencils.

Texts/References:

1. G.W. Stewart and J. G. Sun, Matrix Perturbation Theory, Academic Press, 1990
2. B. V. Limaye, Spectral Perturbation and Approximation with Numerical Experiments, Proceedings of CMA, Australian National University, Vol.13, 1986.
3. T. Kato, Perturbation Theory for Linear operators, Springer, 1980.
4. F. R. Gantmacher, Applications of the Theory of Matrices, Dover, 2005.