Skip to main content
SpringerLink
Log in
Birkhäuser

Indefinite Linear Algebra and Applications

  • Textbook
  • © 2005

Overview

Authors:
  1. Israel Gohberg

    1. School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv, Israel

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Peter Lancaster

    1. Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada

    View author publications

    You can also search for this author in PubMed   Google Scholar

  3. Leiba Rodman

    1. Department of Mathematics, College of William and Mary, Williamsburg, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Thorough treatment of indefinite inner product spaces
  • Combining modern linear algebra with systems theory
  • Suitable as reference work for scientists and engineers

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (14 chapters)

  1. Front Matter

    Pages i-xii
    Download chapter PDF

  2. Introduction and Outline

    Pages 1-6

  3. Indefinite Inner Products

    Pages 7-18

  4. Orthogonalization and Orthogonal Polynomials

    Pages 19-44

  5. Classes of Linear Transformations

    Pages 45-72

  6. Canonical Forms

    Pages 73-123

  7. Real H-Selfadjoint Matrices

    Pages 125-142

  8. Functions of H-Selfadjoint Matrices

    Pages 143-158

  9. H-Normal Matrices

    Pages 159-177

  10. General Perturbations. Stability of Diagonalizable Matrices

    Pages 179-205

  11. Definite Invariant Subspaces

    Pages 207-228

  12. Differential Equations of First Order

    Pages 229-236

  13. Matrix Polynomials

    Pages 237-266

  14. Differential and Difference Equations of Higher Order

    Pages 267-288

  15. Algebraic Riccati Equations

    Pages 289-318

  16. Back Matter

    Pages 319-357
    Download chapter PDF
Back to top

Keywords

About this book

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.

Reviews

This is a splendidly written book, one of a number by three of the world’s leading linear algebraists, that collects many results on indefinite linear algebra from the literature and puts them all in a single place. The book is based in part on a 1983 book titled Matrices and Indefinite Scalar Products by the same authors and publisher but includes many contemporary results from the journal literature and elsewhere. In fact, the ends of many of the chapters provide a guide to sources where further materials are to be found. There are some excellent exercises collected at the end of each chapter making the book ideal as a graduate-level textbook.

(SIAM Review)

"The reviewer is convinced that the present book will be welcome by all readers interested in applications of indefinite linear algebra in matrix polynomials, differential equations and difference equations with constant coefficients." Mircea Crâsmareanu, Analele Stiintifice

Authors and Affiliations

  • School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv, Israel

    Israel Gohberg

  • Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada

    Peter Lancaster

  • Department of Mathematics, College of William and Mary, Williamsburg, USA

    Leiba Rodman

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation