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:[1] 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. More generally, for Banach spaces(typically denoted by

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