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.
Author(s): Israel Gohberg, Peter Lancaster, Leiba Rodman
Edition: 1
Publisher: Birkhäuser Basel
Year: 2005
Language: English
Pages: 362
front-matter.pdf......Page 1
1 Introduction and Outline.pdf......Page 10
2 Indefinite Inner Products.pdf......Page 16
3 Orthogonalization and Orthogonal Polynomials.pdf......Page 28
4 Classes of Linear Transformations.pdf......Page 54
5 Canonical Forms.pdf......Page 82
6 Real H-Selfadjoint Matrices.pdf......Page 133
7 Functions of H-Selfadjoint Matrices.pdf......Page 151
8 H-Normal Matrices.pdf......Page 167
9 General Perturbations. Stability of Diagonalizable Matrices.pdf......Page 186
10 Definite Invariant Subspaces.pdf......Page 213
11 Differential Equations of First Order.pdf......Page 235
12 Matrix Polynomials.pdf......Page 243
13 Differential and Difference Equations of Higher Order.pdf......Page 273
14 Algebraic Riccati Equations.pdf......Page 295
back-matter.pdf......Page 325
