Indefinite Linear Algebra and Applications

✍ Scribed by Israel Gohberg, Peter Lancaster, Leiba Rodman

• Publisher: Birkhäuser
• Year: 2005
• Tongue: English
• Leaves: 363
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

00front-matter......Page 1
01Introduction and Outline......Page 11
02Indefinite Inner Products......Page 17
03Orthogonalization and Orthogonal Polynomials......Page 29
04Classes of Linear Transformations......Page 55
05Canonical Forms......Page 83
06Real H-Selfadjoint Matrices......Page 134
07Functions of H-Selfadjoint Matrices......Page 152
08H-Normal Matrices......Page 168
09General Perturbations. Stability of Diagonalizable Matrices......Page 187
10Definite Invariant Subspaces......Page 214
11Differential Equations of First Order......Page 236
12Matrix Polynomials......Page 244
13Differential and Difference Equations of Higher Order......Page 274
14Algebraic Riccati Equations......Page 296
back-matter......Page 326