Pseudospectrum

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 ε-pseudospectrum of a matrix "A" 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".