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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.


  1. ^ Hogben, Leslie (2013). Handbook of Linear Algebra, Second Edition. CRC Press. p. 23-1. ISBN 9781466507296. Retrieved 8 September 2017.
  • Pseudospectra Gateway / Embree and Trefethen [1]