Synopses & Reviews
This book provides a comprehensive treatment of the theory of matrix polynomials. The theory developed here is a natural extension to polynomials of higher degrees, and forms an important new part of linear algebra for which the main concepts and results have been arrived at during the past five years.
Table of Contents
Preface. Introduction. Linearization and Standard Pairs. Representation of Monic Matrix Polynomials. Multiplication and Divisibility. Spectral Divisors and Canonical Factorization. Perturbation and Stability of Divisors. Extension Problems. Spectral Properties and Representations. Applications to Differential and Difference Equations. Least Common Multiples and Greatest Common Divisors of Matrix Polynomials. General Theory. Factorization of Self-Adjoint Matrix Polynomials. Further Analysis of the Sign Characteristic. Quadratic Self-Adjoint Polynomials. The Smith Form and Related Problems. The Matrix Equation AX-XB=C. One Sided and Generalized Inverses. Stable Invariant Subspaces. Indefinite Scalar product Spaces. Analytic Matrix Functions. References.