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

本文致力于研究结构化扰动下结构化矩阵的特征值、Jordan结构和互补不变子空间的保持。确定扰动和保持结构的扰动，使得扰动矩阵将给定子空间再现为不变子空间并保留未扰动矩阵的一对互补不变子空间。这些结果进一步用于获得结构保持扰动，这些扰动修改给定结构矩阵的某些特征值并重现一组所需的特征值，同时保持约旦链不变。此外，获得了一个结构化矩阵的无溢出结构化扰动，其秩等于被修改的特征值（包括多重性）的数量，同时保留其余的特征值和不需要知道的相应 Jordan 链。本文中考虑的特定结构矩阵形成了对应于正对称标量积的李代数和乔丹代数。