Generalizing Eigenvalue Theorems to Pseudospectra Theorems
- 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.
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