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This paper is devoted to the study of preservation of eigenvalues, Jordanstructure and complementary invariant subspaces of structured matrices understructured perturbations. Perturbations and structure-preserving perturbationsare determined such that a perturbed matrix reproduces a given subspace as aninvariant subspace and preserves a pair of complementary invariant subspaces ofthe unperturbed matrix. These results are further utilized to obtainstructure-preserving perturbations which modify certain eigenvalues of a givenstructured matrix and reproduce a set of desired eigenvalues while keeping theJordan chains unchanged. Moreover, a no spillover structured perturbation of astructured matrix is obtained whose rank is equal to the number of eigenvalues(including multiplicities) which are modified, and in addition, preserves therest of the eigenvalues and the corresponding Jordan chains which need not beknown. The specific structured matrices considered in this paper form Jordanand Lie algebra corresponding to an orthosymmetric scalar product.

Preserving spectral properties of structured matrices under structured perturbations