Spectra and Pseudospectra: The Behavior of Nonnormal Matrices and Operators by Trefethen, Lloyd N., Embree, Mark (2005) Hardcover

by Lloyd N. Trefethen

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 is the authoritative 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.

Genres: Mathematics

Hardcover

First published July 18, 2005

Reviews

[William · Rating 5 out of 5]

The book to learn the material from, and a refreshingly engaging book. The authors are correct that the pictures are worth looking at even for the chapters that you cannot find an excuse to read. That said, the tools that the book teaches are extremely useful for the analysis of non-normal linear systems.

For someone reading the material with an eye to studying ordinary differential equations, the introductory part (Part I), the part on transience (Part IV), certain sections from the part on numerics (Part VII), and certain odd bits throughout would all be useful (in Part X and XI). But I couldn't help but be drawn in by several of the sections that were not written for me, the material on fluid mechanics makes me want to learn more about the subject so I could do work along similar lines. Other work was simply entertaining to read, such as the two chapters on Markov processes and the cut-off phenomenon, and the part on random matrices.