On condition numbers and pseudo spectrum for multiparameter eigenvalue problems

We investigate the behavior of multiparameter eigenvalues undersome type of matrices(we call class) perturbations. We show for manyclass in complex (symmetric,skew symmetric, Hermitian, skew Hermitian,persymmetic, Toeplitz, symmetric Toeplitz, Hankel, persymmetricHankel, Circulant) the classed condition number is equal to the unclassedcondition number for 2-norm, and prove similar results for realperturbations. An exception is complex skewsymmetric matrices. Wealso prove that classed pseudospctra for multiparameter eigenvalues isequal to unclassed pseudospectra, here class Hermitian and skew Hermitianmatrices are exceptional.