Spectra and Pseudospectra

The Behavior of Nonnormal Matrices and Operators

Lloyd N. Trefethen, Mark Embree

• Publisher: Princeton University Press
• Year: 2020
• ISBN:
  9780691213101
• Topic: Mathematics
• Subtopic: Algebra
• Index: Mathematics

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.

Table of contents

• Cover Page
• Half-title Page
• Title Page
• Copyright Page
• Dedication
• Contents
• Preface
• Acknowledgments
• I. Introduction
• II. Toeplitz Matrices
• III. Differential Operators
• IV. Transient Effects and Nonnormal Dynamics
• V. Fluid Mechanics
• VI. Matrix Iterations
• VII. Numerical Solution of Differential Equations
• VIII. Random Matrices
• IX. Computation of Pseudospectra
• X. Further Mathematical Issues
• XI. Further Examples and Applications
• References
• Index