By I. Gohberg
This e-book offers a accomplished remedy of the idea of polynomials in a fancy variable with matrix coefficients. uncomplicated matrix idea will be considered because the research of the precise case of polynomials of first measure; the speculation built in Matrix Polynomials is a ordinary extension of this example to polynomials of upper measure. It has purposes in lots of parts, equivalent to differential equations, platforms conception, the Wiener Hopf method, mechanics and vibrations, and numerical research. even though there were major advances in a few quarters, this paintings is still the one systematic improvement of the idea of matrix polynomials.
Audience: The ebook is suitable for college students, teachers, and researchers in linear algebra, operator concept, differential equations, structures concept, and numerical research. Its contents are available to readers who've had undergraduate-level classes in linear algebra and complicated analysis.
Contents: Preface to the Classics variation; Preface; Errata; advent; half I: Monic Matrix Polynomials: bankruptcy 1: Linearization and conventional Pairs; bankruptcy 2: illustration of Monic Matrix Polynomials; bankruptcy three: Multiplication and Divisability; bankruptcy four: Spectral Divisors and Canonical Factorization; bankruptcy five: Perturbation and balance of Divisors; bankruptcy 6: Extension difficulties; half II: Nonmonic Matrix Polynomials: bankruptcy 7: Spectral homes and Representations; bankruptcy eight: purposes to Differential and distinction Equations; bankruptcy nine: Least universal Multiples and maximum universal Divisors of Matrix Polynomials; half III: Self-Adjoint Matrix Polynomials: bankruptcy 10: basic idea; bankruptcy eleven: Factorization of Self-Adjoint Matrix Polynomials; bankruptcy 12: additional research of the signal attribute; bankruptcy thirteen: Quadratic Self-Adjoint Polynomials; half IV: Supplementary Chapters in Linear Algebra: bankruptcy S1: The Smith shape and similar difficulties; bankruptcy S2: The Matrix Equation AX XB = C; bankruptcy S3: One-Sided and Generalized Inverses; bankruptcy S4: sturdy Invariant Subspaces; bankruptcy S5: Indefinite Scalar Product areas; bankruptcy S6: Analytic Matrix services; References; checklist of Notation and Conventions; Index