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ISBN 13: 9783764373498
Author: Israel Gohberg, Peter Lancaster, Leiba Rodman
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.
Introduction and Outline
Indefinite Inner Products
Orthogonalization and Orthogonal Polynomials
Classes of Linear Transformations
Canonical Forms
Real H-Selfadjoint Matrices
Functions of H-Selfadjoint Matrices
H-Normal Matrices
General Perturbations. Stability of Diagonalizable Matrices
Definite Invariant Subspaces
Differential Equations of First Order
Matrix Polynomials
Differential and Difference Equations of Higher Order
Algebraic Riccati Equations
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Tags: Israel Gohberg, Peter Lancaster, Leiba Rodman, Indefinite, algebra
