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Matrix Polynomials

Matrix Polynomials

£73.00

Part of Classics in Applied Mathematics

  • 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

£ 73.00
Paperback

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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.

    • 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.

  • Authors

    I. Gohberg, Tel-Aviv University
    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, University of Calgary
    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, College of William and Mary, Virginia
    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.

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