Structured mapping problems for linearly structured matrices
Abstract
Given an appropriate class of structured matrices S; we characterize matrices X and B for which there exists a matrix A ∈ S such that AX = B and determine all matrices in S mapping X to B. We also determine all matrices in S 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.
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