Spectra and Pseudospectra: The Behavior of Nonnormal Matrices and Operators

(Hardback)

Publishing Details

Classifications

Physical Properties

Description

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.

Reviews

Honorable Mention for the 2005 Award for Best Professional/Scholarly Book in Mathematics and Statistics, Association of American Publishers "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."--Current Engineering Practice "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 Bttcher, Linear Algebra and its Applications "The book contains good introductions to a wide variety of application areas and research topics and is a very appropriate text for a graduate-level seminar. For those interested in pursuing these topics further, the bibliography is an absolute treasure!... It is an invaluable resource for anyone working in the area of nonnormal matrices and linear operators or for anyone involved in an application where nonnormality is important."--Anne Greenbaum, SIAM Review "We suggest ... strongly that the book be opened and read... One will profit by getting considerable insight into a rich variety of phenomena and being acquainted with a large number of beautiful mathematical thoughts."--H. Muthsam Wien, Monatshefte fur Mathematik "The book has been written at a level to be accessible to a wide audience of students of the applied sciences. The subject matter has been carefully referenced, Many illustrations are provided showing an amazing diversity of spectra end pseudospectra. A detailed chapter is provided for those who wish to generate software to approximate the spectrum and pseudospectrum in a particular application."--J. B. Butler, Zentralblatt Math

Author Bio

Lloyd N. Trefethen is Professor of Numerical Analysis and Head of the Numerical Analysis Group at the University of Oxford. Mark Embree is Assistant Professor of Computational and Applied Mathematics at Rice University.