Eigenvalue analysis of non-hermitian matrices and operators can be misleading: Predictions often fail to match observations. Specifically, trouble may arise when the associated sets of eigenvectors are ill-conditioned with respect to the norm of applied interest. In the case of the familiar Euclidean or 2-norm, this means that the matrix or operator is non-normal, and the eigenvectors are not orthogonal. Pseudospectra provide an analytical and graphical alternative for investigating non-normal matrices and operators. Follow the links below to find out more, and please email us with suggestions for additions and improvements.
- Mark Embree, Rice University
and Nick Trefethen, Oxford University
Related sites: Spectral Portraits at CERFACS or Matrix Market; Pseudospectra at Patras

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