论文标题
在结构化扰动下保存结构化矩阵的光谱特性
Preserving spectral properties of structured matrices under structured perturbations
论文作者
论文摘要
本文致力于研究在结构化扰动下结构化矩阵的特征值，约旦结构和互补不变子空间的研究。确定扰动和结构呈现扰动，使得扰动的矩阵将给定的子空间重现为不变子空间，并保留一对未渗透矩阵的互补不变子空间。这些结果进一步用于获得结构保护的扰动，这些扰动会修改给定结构化矩阵的某些特征值，并重现一组所需的特征值，同时使Jordan链保持不变。此外，获得了结构化矩阵的无溢流结构化扰动，其等级等于修改的特征值（包括倍增性），此外，还保留了其余的特征值和相应的Jordan链，这些链条不需要知道。本文中考虑的特定结构矩阵形成了约旦和对应于正异构标量产品的代数。
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, and in addition, preserves the rest of the eigenvalues and the corresponding Jordan chains which need not be known. The specific structured matrices considered in this paper form Jordan and Lie algebra corresponding to an orthosymmetric scalar product.
