Generalizing Eigenvalue Theorems to Pseudospectra Theorems
Mark Embree, Lloyd N. Trefethen · SIAM Journal on Scientific Computing · 2001
Analysis of nonsymmetric matrix iterations based on eigenvalues can be misleading. In this paper, we discuss sixteen theorems involving ${{\varepsilon}}\def\Lam{\Lambda}\def\lam{\lambda}$-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 ${{\varepsilon}}\def\Lam{\Lambda}\def\lam{\lambda}=0$.