Nonderotary矩阵

Nonderotary Matrices

Nonderotary矩阵是一类重要的矩阵，将从相似标准形、中心化子、相似类维数等角度刻划这类矩阵的性质，证明矩阵A是Nonderotary当且仅当与A可交换的所有矩阵都可以写成A的多项式，当且仅当A的相似类的维数最大．

Nonderotary matrices are a class of important matrices. In this note, we charac- terize 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.