## Pseudospectra of linear operators (1997)

Venue: | SIAM Rev |

Citations: | 113 - 8 self |

### BibTeX

@ARTICLE{Trefethen97pseudospectraof,

author = {Lloyd N. Trefethen},

title = {Pseudospectra of linear operators},

journal = {SIAM Rev},

year = {1997},

pages = {383--406}

}

### Years of Citing Articles

### OpenURL

### Abstract

Abstract. If a matrix or linear operator A is far from normal, its eigenvalues or, more generally, its spectrum may have little to do with its behavior as measured by quantities such as ‖An ‖ or ‖exp(tA)‖. More may be learned by examining the sets in the complex plane known as the pseudospectra of A, defined by level curves of the norm of the resolvent, ‖(zI − A) −1‖. Five years ago, the author published a paper that presented computed pseudospectra of thirteen highly nonnormal matrices arising in various applications. Since that time, analogous computations have been carried out for differential and integral operators. This paper, a companion to the earlier one, presents ten examples, each chosen to illustrate one or more mathematical or physical principles.