Eigenvalues of Matrices, Revised Edition (Classics in Applied Mathematics)

This classic textbook provides a modern and complete guide to the calculation of eigenvalues of matrices, written at an accessible level that presents in matrix notation the fundamental aspects of the spectral theory of linear operators in finite dimension.

Unique features of Eigenvalues of Matrices, Revised Edition include the convergence of eigensolvers serving as the basis of the notion of the gap between invariant subspaces, its coverage of the impact of the high nonnormality of the matrix on its eigenvalues, and the comprehensive nature of the material that moves beyond mathematical technicalities to the essential mean carried out by matrix eigenvalues.

The author has added a new chapter that uncovers reasons why matrices are even more fundamental tools than vectors for the information processing that takes place during the dynamical evolution of systems. Some of these ideas appear in print for the first time.

Audience: The book s primary use is as a course text for undergraduate students in mathematics, applied mathematics, physics, and engineering. It is also useful as a reference for researchers or for engineers in high-tech industries who are confronted with instability and chaos in intensive computing that results from the strong coupling of two distinct phenomena.

Contents: Chapter 1: Supplements from Linear Algebra; Chapter 2: Elements of Spectral Theory; Chapter 3: Why Compute Eigenvalues?; Chapter 4: Error Analysis; Chapter 5: Foundations of Methods for Computing Eigenvalues; Chapter 6: Numerical Methods for Large Matrices; Chapter 7: Chebyshev's Iterative Methods; Chapter 8: Polymorphic Information Processing with Matrices; Appendix A: Solution to Exercises; Appendix B: References for Exercises; Appendix C: References