Del i serien Classics in Applied Mathematics

Matrix Polynomials

Häftad, Engelska, 2009

1 649 kr

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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.

Produktinformation

Utgivningsdatum2009-07-30
Mått152 x 229 x 22 mm
Vikt593 g
FormatHäftad
SpråkEngelska
SerieClassics in Applied Mathematics
Antal sidor433
FörlagSociety for Industrial & Applied Mathematics,U.S.
ISBN9780898716818

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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.

Preface to the Classics EditionPrefaceErrataIntroductionPart I: Monic Matrix Polynomials: Chapter 1: Linearization and Standard PairsChapter 2: Representation of Monic Matrix PolynomialsChapter 3: Multiplication and DivisabilityChapter 4: Spectral Divisors and Canonical FactorizationChapter 5: Perturbation and Stability of DivisorsChapter 6: Extension ProblemsPart II: Nonmonic Matrix Polynomials: Chapter 7: Spectral Properties and RepresentationsChapter 8: Applications to Differential and Difference EquationsChapter 9: Least Common Multiples and Greatest Common Divisors of Matrix PolynomialsPart III: Self-Adjoint Matrix Polynomials: Chapter 10: General TheoryChapter 11: Factorization of Self-Adjoint Matrix PolynomialsChapter 12: Further Analysis of the Sign CharacteristicChapter 13: Quadratic Self-Adjoint PolynomialsPart IV: Supplementary Chapters in Linear Algebra: Chapter S1: The Smith Form and Related ProblemsChapter S2: The Matrix Equation AX – XB = CChapter S3: One-Sided and Generalized InversesChapter S4: Stable Invariant SubspacesChapter S5: Indefinite Scalar Product SpacesChapter S6: Analytic Matrix FunctionsReferencesList of Notation and ConventionsIndex