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Matrix PolynomialsMatrix Polynomials

I. Gohberg, P. Lancaster, and L. Rodman



Classics in Applied Mathematics 58

This book provides a comprehensive treatment of the theory of polynomials in a complex variable with matrix coefficients. Basic matrix theory can be viewed as the study of the special case of polynomials of first degree; the theory developed in Matrix Polynomials is a natural extension of this case to polynomials of higher degree. It has applications in many areas, such as differential equations, systems theory, the Wiener–Hopf technique, mechanics and vibrations, and numerical analysis. Although there have been significant advances in some quarters, this work remains the only systematic development of the theory of matrix polynomials.

Audience
The book is appropriate for students, instructors, and researchers in linear algebra, operator theory, differential equations, systems theory, and numerical analysis. Its contents are accessible to readers who have had undergraduate-level courses in linear algebra and complex analysis.

Contents
Preface to the Classics Edition;
Preface;
Errata;
Introduction;
Part I: Monic Matrix Polynomials:
Chapter 1: Linearization and Standard Pairs;
Chapter 2: Representation of Monic Matrix Polynomials;
Chapter 3: Multiplication and Divisability;
Chapter 4: Spectral Divisors and Canonical Factorization;
Chapter 5: Perturbation and Stability of Divisors;
Chapter 6: Extension Problems;
Part II: Nonmonic Matrix Polynomials:
Chapter 7: Spectral Properties and Representations;
Chapter 8: Applications to Differential and Difference Equations;
Chapter 9: Least Common Multiples and Greatest Common Divisors of Matrix Polynomials;
Part III: Self-Adjoint Matrix Polynomials:
Chapter 10: General Theory;
Chapter 11: Factorization of Self-Adjoint Matrix Polynomials;
Chapter 12: Further Analysis of the Sign Characteristic;
Chapter 13: Quadratic Self-Adjoint Polynomials;
Part IV: Supplementary Chapters in Linear Algebra:
Chapter S1: The Smith Form and Related Problems;
Chapter S2: The Matrix Equation AX – XB = C;
Chapter S3: One-Sided and Generalized Inverses;
Chapter S4: Stable Invariant Subspaces;
Chapter S5: Indefinite Scalar Product Spaces;
Chapter S6: Analytic Matrix Functions;
References;
List of Notation and Conventions;
Index

About the Authors
I. Gohberg is Professor Emeritus of Tel-Aviv University and Free University of Amsterdam and Doctor Honoris Causa of several European universities. He has contributed to the fields of functional analysis and operator theory, integral equations and systems theory, matrix analysis and linear algebra, and computational techniques for structured integral equations and structured matrices. He has coauthored 25 books in different areas of pure and applied mathematics.

P. Lancaster is Professor Emeritus and Faculty Professor in the Department of Mathematics and Statistics at the University of Calgary. His research interests are mainly in matrix analysis and linear algebra as applied to vibrating systems, systems and control theory, and numerical analysis. He has published prolifically in the form of monographs, texts, and journal publications.

L. Rodman is Professor of Mathematics at the College of William and Mary. He has done extensive work in matrix analysis, operator theory, and related fields. He has authored one book, co-authored six others, and served as a co-editor of several volumes.

Keywords
spectral theory of matrix polynomials and applications

2009 / xxiv + 409 pages / Softcover
ISBN: 978-0-898716-81-8
List Price $95.00/ SIAM Member Price $66.50/ Order Code CL58
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