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.
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.
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.
Inhaltsangabe
1. Preface to the Classics Edition 2. Preface 3. Errata 4. Introduction 5. Part I: Monic Matrix Polynomials: Chapter 1: Linearization and Standard Pairs 6. Chapter 2: Representation of Monic Matrix Polynomials 7. Chapter 3: Multiplication and Divisability 8. Chapter 4: Spectral Divisors and Canonical Factorization 9. Chapter 5: Perturbation and Stability of Divisors 10. Chapter 6: Extension Problems 11. Part II: Nonmonic Matrix Polynomials: Chapter 7: Spectral Properties and Representations 12. Chapter 8: Applications to Differential and Difference Equations 13. Chapter 9: Least Common Multiples and Greatest Common Divisors of Matrix Polynomials 14. Part III: Self-Adjoint Matrix Polynomials: Chapter 10: General Theory 15. Chapter 11: Factorization of Self-Adjoint Matrix Polynomials 16. Chapter 12: Further Analysis of the Sign Characteristic 17. Chapter 13: Quadratic Self-Adjoint Polynomials 18. Part IV: Supplementary Chapters in Linear Algebra: Chapter S1: The Smith Form and Related Problems 19. Chapter S2: The Matrix Equation AX – XB = C 20. Chapter S3: One-Sided and Generalized Inverses 21. Chapter S4: Stable Invariant Subspaces 22. Chapter S5: Indefinite Scalar Product Spaces 23. Chapter S6: Analytic Matrix Functions 24. References 25. List of Notation and Conventions 26. Index
1. Preface to the Classics Edition 2. Preface 3. Errata 4. Introduction 5. Part I: Monic Matrix Polynomials: Chapter 1: Linearization and Standard Pairs 6. Chapter 2: Representation of Monic Matrix Polynomials 7. Chapter 3: Multiplication and Divisability 8. Chapter 4: Spectral Divisors and Canonical Factorization 9. Chapter 5: Perturbation and Stability of Divisors 10. Chapter 6: Extension Problems 11. Part II: Nonmonic Matrix Polynomials: Chapter 7: Spectral Properties and Representations 12. Chapter 8: Applications to Differential and Difference Equations 13. Chapter 9: Least Common Multiples and Greatest Common Divisors of Matrix Polynomials 14. Part III: Self-Adjoint Matrix Polynomials: Chapter 10: General Theory 15. Chapter 11: Factorization of Self-Adjoint Matrix Polynomials 16. Chapter 12: Further Analysis of the Sign Characteristic 17. Chapter 13: Quadratic Self-Adjoint Polynomials 18. Part IV: Supplementary Chapters in Linear Algebra: Chapter S1: The Smith Form and Related Problems 19. Chapter S2: The Matrix Equation AX – XB = C 20. Chapter S3: One-Sided and Generalized Inverses 21. Chapter S4: Stable Invariant Subspaces 22. Chapter S5: Indefinite Scalar Product Spaces 23. Chapter S6: Analytic Matrix Functions 24. References 25. List of Notation and Conventions 26. Index
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