广义特征值定理向伪谱定理的推广

Generalization of Generalized Eigenvalue Theorems to Pseudospectra Theorems

特征值 (谱)对分析非正规矩阵或算子是一个不完美的工具。作为谱的自然延伸,伪谱是一个针对非正规系统的新工具。该文讨论了 5个包含ε 伪谱的定理,每个定理都是对熟悉的广义特征值定理的推广。在对高度非正规矩阵的研究应用中,这些定理将比它们的特例———广义特征值定理更可靠,能提供更多的信息。

Eigenvalues, more generally, spectra, are an imperfect tool for analyzing nonnormal matrices and operators. As a natural extension of the idea of spectra, pseudospectra is a new tool for nonnormal system. This paper discussed five theorems involving ε-pseudospectra. Each generalizes a familiar generalized eigenvalue theorem. In the practical applications of highly nonnormal matrices, these theorems may be more useful than their generalized eigenvalue special cases and may provide more descriptive information.