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 operatorss and their eigenfunctions.

The -pseudospectrum of a matrix A consists of all eigenvalues of matrices which are -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.

More generally, for Banach spaces) in the following way

is not invertible.

References

Bibliography

• Lloyd N. Trefethen and Mark Embree: "Spectra And Pseudospectra: The Behavior of Nonnormal Matrices And Operators", Princeton Univ. Press, (2005).

External links

• Pseudospectra Gateway by Embree and Trefethen