矩阵扶正器中对合的乘积

Pub Date : 2022-08-20 DOI:10.13001/ela.2022.7091

Ralph John de la Cruz, Raymond Louis Tañedo

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引用次数: 1

摘要

一个方阵$A$是一个对合矩阵，如果$A^{2} = I$。用$\mathscr{C}(S)$表示的方阵$S$的中心化器是在特征不等于2的代数闭域上满足$AS = SA$的所有$ a $的集合。我们确定了$A \in \mathscr{C}(S)$是$\mathscr{C}(S)$的对合积的充要条件，其中$S$是一个长度为3的齐次Weyr结构的基本Weyr矩阵。最后，我们将给出Weyr结构长度大于3时的一些结果。

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The products of involutions in a matrix centralizer

A square matrix $A$ is an involution if $A^{2} = I$. The centralizer of a square matrix $S$ denoted by $\mathscr{C}(S)$ is the set of all $A$ such that $AS = SA$ over an algebraically closed field of characteristic not equal to 2. We determine necessary and sufficient conditions for $A \in \mathscr{C}(S)$ to be a product of involutions in $\mathscr{C}(S)$ where $S$ is a basic Weyr matrix with homogeneous Weyr structure of length 3. Finally, we will show some results for the case when the length of the Weyr structure is greater than 3.

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