Structured pseudospectra and structured sensitivity of eigenvalues

Pseudospectra and structured pseudospectra have been investigated widely. In this paper, for the matrix spectral norm we give a new equivalent definition of structured pseudospectra of a matrix triplet (A,B,C)(A,B,C) via the so-called restricted singular value decomposition (RSVD). According to this definition we provide a solution of structured Wilkinson's problem, which concerns structured sensitivity of eigenvalues of square matrices. Several examples are given to illustrate our results. Also, we extend the new definition of structured pseudospectra to polynomial eigenvalue problems.