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 εΛλ-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 εΛλ=0.