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Nonderotary matrices. (Chinese. English summary) Zbl 1413.15060

Summary: Nonderotary matrices are a class of important matrices. In this note, we characterize Nonderotary matrices in the aspect of canonical forms under similarity, centralizers and dimensions of similarity classes, and show that \(A\) is Nonderotary if and only if all matrices commutating with \(A\) can be written as some polynomial of \(A\), and if and only if the dimension of the similarity class of \(A\) takes the maximal value.

MSC:

15B99 Special matrices
15A27 Commutativity of matrices
15A21 Canonical forms, reductions, classification
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