Matrix Polynomials
£73.00
Part of Classics in Applied Mathematics
- Authors:
- I. Gohberg, Tel-Aviv University
- P. Lancaster, University of Calgary
- L. Rodman, College of William and Mary, Virginia
- Date Published: July 2009
- availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
- format: Paperback
- isbn: 9780898716818
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This book is the definitive 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. 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.
Read more- A true classic, this is the only systematic development of the theory of matrix polynomials; nothing has come close for 20 years
- Includes applications to differential and difference equations
- Written for a wide audience of student and practising engineers, scientists, and mathematicians
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×Product details
- Date Published: July 2009
- format: Paperback
- isbn: 9780898716818
- length: 184 pages
- dimensions: 228 x 152 x 22 mm
- weight: 0.59kg
- availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
Table of Contents
Preface to the Classics Edition
Preface
Errata
Introduction
Part I. Monic Matrix Polynomials:
1. Linearization and standard pairs
2. Representation of monic matrix polynomials
3. Multiplication and divisibility
4. Spectral divisors and canonical factorization
5. Perturbation and stability of divisors
6. Extension problems
Part II. Nonmonic Matrix Polynomials:
7. Spectral properties and representations
8. Applications to differential and difference equations
9. Least common multiples and greatest common divisors of matrix polynomials
Part III. Self-Adjoint Matrix Polynomials:
10. General theory
11. Factorization of self-adjoint matrix polynomials
12. Further analysis of the sign characteristic
13: Quadratic self-adjoint polynomials
Part IV. Supplementary Chapters in Linear Algebra: S1. The Smith form and related problems
S2. The matrix equation AX – XB = C
S3. One-sided and generalized inverses
S4. Stable invariant subspaces
S5. Indefinite scalar product spaces
S6. Analytic matrix functions
References
List of notation and conventions
Index.
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