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.
Author(s): Israel Gohberg, Peter Lancaster, Leiba Rodman
Edition: 1
Publisher: Birkhäuser Basel
Year: 2005
Language: English
Pages: 371
Tags: Математика;Линейная алгебра и аналитическая геометрия;Линейная алгебра;
Cover......Page 1
Indefinite
Linear Algebra
and
Applications......Page 4
ISBN 9783764373498......Page 5
Preface......Page 8
Contents......Page 10
1
Introduction and Outline......Page 15
2
Indefinite Inner Products......Page 21
3
Orthogonalization and
Orthogonal Polynomials......Page 33
4
Classes of Linear
Transformations......Page 59
5
Canonical Forms......Page 87
6
Real H-Selfadjoint Matrices......Page 139
7
Functions of H-Selfadjoint
Matrices......Page 157
8
H-Normal Matrices......Page 173
9
General Perturbations. Stability
of Diagonalizable Matrices......Page 193
10
Definite Invariant Subspaces......Page 221
11
Differential Equations of First
Order......Page 243
12
Matrix Polynomials......Page 251
13
Differential and Difference
Equations of Higher Order......Page 281
14
Algebraic Riccati Equations......Page 303
A
Topics from Linear Algebra......Page 333
Bibliography......Page 363
Index......Page 369
