Spectra and Pseudospectra The Behavior of Nonnormal Matrices and Operators [Hardcover]

Pure and applied mathematicians, physicists, scientists, and engineers use matrices and operators and their eigenvalues in quantum mechanics, fluid mechanics, structural analysis, acoustics, ecology, numerical analysis, and many other areas. However, in some applications the usual analysis based on eigenvalues fails. For example, eigenvalues are often ineffective for analyzing dynamical systems such as fluid flow, Markov chains, ecological models, and matrix iterations. That's where this book comes in.

This istheauthoritative work on nonnormal matrices and operators, written by the authorities who made them famous. Each of the sixty sections is written as a self-contained essay. Each document is a lavishly illustrated introductory survey of its topic, complete with beautiful numerical experiments and all the right references. The breadth of included topics and the numerous applications that provide links between fields will make this an essential reference in mathematics and related sciences.

"Honorable Mention for the 2005 Award for Best Professional/Scholarly Book in Mathematics and Statistics, Association of American Publishers"Lloyd N. Trefethenis Professor of Numerical Analysis and Head of the Numerical Analysis Group at the University of Oxford.Mark Embreeis Assistant Professor of Computational and Applied Mathematics at Rice University. This is the authoritative work on nonnormal matrices and operators, written by the authorities who made them famous. Their decision to prepare this volume is indeed a momentous event. The overall organization of the book is a methodological masterpiece. The splitting of the huge amount of material into sixty short self-contained essays is extremely reader-friendly. The writing is extremely lucid and intriguing. . . . The many figures illustrate the mathematics in an unusually fascinating way. ---Albrecht B?ttcher,Linear Algebra and its Applications The book cl©