Eigenvalues of Matrices (2^nd Ed.)
Classics in Applied Mathematics Series

This revised edition of a classic textbook provides a complete guide to the calculation of eigenvalues of matrices. Written at an accessible level, this modern exposition of the subject presents fundamental aspects of the spectral theory of linear operators in finite dimension. Unique features of this book include a treatment of the convergence of eigensolvers based on the notion of the gap between invariant subspaces, and coverage of the impact of the high nonnormality of a matrix on its eigenvalues. Also included is a new chapter uncovering reasons why matrices are fundamental tools for the information processing that takes place in the dynamical evolution of systems. Some of these ideas appear in print for the first time. The book's primary use is as a course text for undergraduate students in mathematics, applied mathematics, physics and engineering. It is also a useful reference for researchers and engineers in industry.

Preface to the classics edition; Preface; Preface to the English edition; Notation; List of errata; 1. Supplements from linear algebra; 2. Elements of spectral theory; 3. Why compute eigenvalues?; 4. Error analysis; 5. Foundations of methods for computing eigenvalues; 6. Numerical methods for large matrices; 7. Chebyshev's iterative methods; 8. Polymorphic information processing with matrices; Appendix A. Solution to exercises; Appendix B. References for exercises; Appendix C. References; Index.

Françoise Chatelin is Professor of Mathematics at the University of Toulouse and head of the Qualitative Computing Group at CERFACS. Before moving to CERFACS, she was a professor at the universities of Grenoble and Paris IX Dauphine. She also worked for a decade in the industrial research laboratories of IBM France and Thales, where she was in charge of intensive computing activities. Her areas of expertise include spectral theory for linear operators in Banach spaces and finite precision computation of very large eigenproblems. She currently explores the uncharted domain of mathematical computation that lies beyond real or complex analysis.