On structured pseudo spectra for polynomial eigenvalue problems

Pseudospectra associated with the generalized eigenvalue problemshave been widely investigated in recent years. This paper is organizedas follows. First, we prove for a class∈{Symmetric, Persymmetric,Toeplitz, SymToeplitz, Hankel, PersymHankel, Circulant}, we havethe classed pseudospectrum of matrix is equal to the unclassed pseudospectrumbecause of the departure from singularity. Second, we provethe same results for classed pseudospectra of matrix polynomials.