Indefinite Linear Algebra and Applications

ISBN-13: 9783764373498 / Angielski / Miękka / 2005 / 372 str.

Israel Gohberg; Peter Lancaster; Leiba Rodman

Opis

This book covers recent results in linear algebra with indefinite inner product. It includes applications to differential and difference equations with symmetries, matrix polynomials and Riccati equations. These applications are based on linear algebra in spaces with indefinite inner product. The latter forms an independent branch of linear algebra called indefinite linear algebra. This new subject is presented following the principles of a standard linear algebra course.

Recenzje

This is a splendidly written book, one of a number by three of the world's leading linear algebraists, that collects many results on indefinite linear algebra from the literature and puts them all in a single place. The book is based in part on a 1983 book titled Matrices and Indefinite Scalar Products by the same authors and publisher but includes many contemporary results from the journal literature and elsewhere. In fact, the ends of many of the chapters provide a guide to sources where further materials are to be found. There are some excellent exercises collected at the end of each chapter making the book ideal as a graduate-level textbook.

(SIAM Review)

"The reviewer is convinced that the present book will be welcome by all readers interested in applications of indefinite linear algebra in matrix polynomials, differential equations and difference equations with constant coefficients." Mircea Crâsmareanu, Analele Stiintifice

Spis treści

Preface.- 1. Introduction and Outline.- 2. Indefinite Inner Products.- 3. Orthogonalization and Orthogonal Polynomials.- 4. Classes of Linear Transformations.- 5. Canonical Forms.- 6. Real H-Selfadjoint Matrices.- 7. Functions of H-Selfadjoint Matrices.- 8. H-Normal Matrices.- 9. General Perturbations. Stability of Diagonalizable Matrices.- 10. Definite Invariant Subspaces.- 11. Differential Equations of First Order.- 12. Matrix Polynomials.- 13. Differential and Difference Equations of Higher Order.- 14. Algebraic Riccati Equations.- Appendix: Topics from Linear Algebra.- Bibliography.- Index

Blurb

This book is dedicated to relatively recent results in linear algebra with indefinite inner product. It also includes applications to differential and difference equations with symmetries, matrix polynomials and Riccati equations. These applications have been developed in the last fifty years, and all of them are based on linear algebra in spaces with indefinite inner product. The latter forms a new more or less independent branch of linear algebra and we gave it the name of indefinite linear algebra. This new subject in linear algebra is presented following the lines and principles of a standard linear algebra course.
This book has the structure of a graduate text in which chapters of advanced linear algebra form the core. This together with the many significant applications and accessible style will make it widely useful for engineers, scientists and mathematicians alike.