结构伪特征值的重数
Multiplicities of the structured pseudoeigenvalues
摘要：
矩阵A的结构化伪谱是复数的集合，这些复数是矩阵X的特征值，这些特征值接近A并且在固定的位置集合处具有与A相同的元素。在A的结构伪谱的每个连通分量内X的本征值的重数之和不依赖于X。这一事实是众所周知的，但并不像它应该的那样多。为此，我们在这里给出了结果的一个初等而详细的证明。
英文摘要：
The structured pseudospectra of a matrix A are sets of complex numbers that are eigenvalues of matrices X which are near to A and have the same entries as A at a fixed set of places. The sum of multiplicities of the eigenvalues of X inside each connected component of the structured pseudospectra of A does not depend on X. This fact is known, but not so much as it should be. For this reason, we give here an elementary and detailed proof of the result.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
