Matrix Polynomials

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 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 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.

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.