The Pseudo-Spectrum Theory

Pseudo-spectra, developed and popularized mainly by Trefethen and his co-authors, are an important tool for assessing the global sensitivity of matrix eigenvalues to perturbations in the matrix. Most research has emphasised on pseudospectra of standard and generalized eigenvalue problems. Pseudospectra for square matrix polynomials are defined and characterized by Tisseur and Higham, Higham and Tisseur, and Lancaster and Psarrakos, for the generalization of the 𝜖-pseudo-spectrum to matrix polynomials.