Indefinite linear algebra and applications

著者

書誌事項

Indefinite linear algebra and applications

Israel Gohberg, Peter Lancaster, Leiba Rodman

Birkhauser, c2005

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  • : ebook

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注記

Includes bibliographical references and index

内容説明・目次

内容説明

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.

目次

Preface.- 1. Introduction and Outline.- 2. Indefinite Inner Products.- 3. Orthogonalization and Orthogonal Polynomials.- 4. Classes of Linear Transformations.- 5. Canonical Forms.- 6. Real H-Selfadjoint Matrices.- 7. Functions of H-Selfadjoint Matrices.- 8. H-Normal Matrices.- 9. General Perturbations. Stability of Diagonalizable Matrices.- 10. Definite Invariant Subspaces.- 11. Differential Equations of First Order.- 12. Matrix Polynomials.- 13. Differential and Difference Equations of Higher Order.- 14. Algebraic Riccati Equations.- Appendix: Topics from Linear Algebra.- Bibliography.- Index

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