ABSTRACT

Given two complex $n\times n$ matrices A and B, necessary and sufficient conditions are presented in order for the null space of A−B to be equal to the total strong common multiplicity of A and B. Using this characterization, when $\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{k}(A-B)=n-1$, a simple characterization for A and B to have a strong common eigenvalue is also obtained.

中文翻译：

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两个矩阵的总强公多重性和 Sylvester 结果

摘要

给定两个复$n\times n$矩阵A和B ，为了使A - B的零空间等于A和B的总强共同多重性，提出了必要和充分条件。使用这种表征，当$\mathrm{r}\mathrm{一个}\mathrm{n}\mathrm{ķ}(\mathrm{一个}-乙)=n-1$，也得到了A和B具有强共同特征值的简单表征。