Franklin

Matrix polynomials [electronic resource] / I. Gohberg, P. Lancaster, L. Rodman.

Author/Creator:
Gohberg, I. (Israel), 1928-
Edition:
SIAM ed., [Classics ed.].
Publication:
Philadelphia, Pa. : Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104), 2009.
Series:
Classics in applied mathematics ; 58.
Classics in applied mathematics ; 58
Format/Description:
Book
1 electronic text (xxiv, 409 p.) : digital file.
Subjects:
Matrices.
Polynomials.
Language:
English
System Details:
Mode of access: World Wide Web.
System requirements: Adobe Acrobat Reader.
Summary:
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: 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:
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
Supplementary chapters in linear algebra:
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.
Notes:
Originally published: New York : Academic Press, 1982.
Includes bibliographical references and index.
Description based on title page of print version.
Contributor:
Society for Industrial and Applied Mathematics.
Lancaster, Peter, 1929-
Rodman, L.
ISBN:
0-89871-902-X
Publisher Number:
CL58 siam
Access Restriction:
Restricted to subscribers or individual electronic text purchasers.
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