# Report

## Generalizing Eigenvalue Theorems to Pseudospectra Theorems

Abstract:
Analysis of nonsymmetric matrix iterations based on eigenvalues can be misleading. In this paper, we discuss sixteen theorems involving $\epsilon$-pseudospectra that each generalize a familiar eigenvalue theorem and may provide more descriptive information in some cases. Our organizing principle is that each pseudospectral theorem reduces precisely to the corresponding eigenvalue theorem when $\epsilon$ = 0. This work was supported by UK Engineering and Physical Sciences Research Council Grant GR/M12414.

### Access Document

Files:
• (pdf, 178.8KB)

### Authors

Publisher:
Unspecified
Publication date:
2000-06-01
UUID:
uuid:24456fda-ae75-4521-8c7f-3b1ed95219d8
Local pid:
oai:eprints.maths.ox.ac.uk:1269
Deposit date:
2011-06-01