In mathematics, the pseudospectrum of an operator is a set containing the spectrum of the operator and the numbers that are "almost" eigenvalues. Knowledge of the pseudospectrum can be particularly useful for understanding non-normal operators and their eigenfunctions.
The pseudospectrum of a matrix A for a given ε consists of all eigenvalues of matrices which are ε-close to A:
Numerical algorithms which calculate the eigenvalues of a matrix give only approximate results due to rounding and other errors. These errors can be described with the matrix E.
- Pseudospectra Gateway / Embree and Trefethen