By I. Gohberg

This ebook offers a entire therapy of the speculation of polynomials in a posh variable with matrix coefficients. simple matrix concept may be seen because the examine of the targeted case of polynomials of first measure; the speculation constructed in Matrix Polynomials is a common extension of this example to polynomials of upper measure. It has functions in lots of components, equivalent to differential equations, platforms idea, the Wiener Hopf procedure, mechanics and vibrations, and numerical research. even if there were major advances in a few quarters, this paintings continues to be the single systematic improvement of the speculation of matrix polynomials.

Audience: The ebook is acceptable for college students, teachers, and researchers in linear algebra, operator thought, differential equations, platforms idea, and numerical research. Its contents are available to readers who've had undergraduate-level classes in linear algebra and intricate analysis.

Contents: Preface to the Classics variation; Preface; Errata; creation; 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: common thought; 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: reliable Invariant Subspaces; bankruptcy S5: Indefinite Scalar Product areas; bankruptcy S6: Analytic Matrix capabilities; References; record of Notation and Conventions; Index

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