Abstract

A known criterion of the congruence between nonsingular matrices (\(A\) and \(B\) are congruent if and only if their cosquares \(A^{-T}A\) and \(B^{-T}B\) are similar) is interpreted from the group-theoretic viewpoint. This interpretation makes it possible to understand why it is the cosquares of \(A\) and \(B\) that participate in the above criterion.

中文翻译：

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从群论的角度看非奇异矩阵的同余性

摘要

非奇异矩阵（\（A \）和\（B \）之间的同余性的已知准则是一致的，当且仅当它们的余平方\（A ^ {-T} A \）和\（B ^ {-T} B \）相似）是从群体理论的角度进行解释的。这种解释使我们有可能理解为什么是上述准则的\（A \）和\（B \）的平方。