Structured mapping problems for linearly structured matrices

Given an appropriate class of structured matrices SS, we characterize matrices X and B   for which there exists a matrix A∈SA∈S such that AX=BAX=B and determine all matrices in SS mapping X to B  . We also determine all matrices in SS mapping X to B and having the smallest norm. We use these results to investigate structured backward errors of approximate eigenpairs and approximate invariant subspaces, and structured pseudospectra of structured matrices.