Indefinite Linear Algebra and Applications

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Springer Science & Business Media, Feb 8, 2006 - Mathematics - 357 pages

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.

 

Contents

Introduction and Outline
1
Indefinite Inner Products
7
Orthogonalization and Orthogonal Polynomials
19
Classes of Linear Transformations
45
Canonical Forms
73
Real HSelfadjoint Matrices
125
Functions of HSelfadjoint Matrices
143
HNormal Matrices
159
Definite Invariant Subspaces
207
Differential Equations of First Order
229
Matrix Polynomials
237
Differential and Difference Equations of Higher Order
267
Algebraic Riccati Equations
289
A Topics from Linear Algebra
319
Bibliography 349
348
237
355

General Perturbations Stability of Diagonalizable Matrices
178

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