矩阵扶正器中对合的乘积

IF 0.7 4区数学 Q2 Mathematics Electronic Journal of Linear Algebra 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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来源期刊

Electronic Journal of Linear Algebra 数学-数学

CiteScore

1.20

自引率

14.30%

发文量

审稿时长

6-12 weeks

期刊介绍： The journal is essentially unlimited by size. Therefore, we have no restrictions on length of articles. Articles are submitted electronically. Refereeing of articles is conventional and of high standards. Posting of articles is immediate following acceptance, processing and final production approval.