矩阵分解为可逆矩阵和固定幂零矩阵的和

IF 0.7 4区数学 Q2 Mathematics

Electronic Journal of Linear Algebra Pub Date : 2023-08-24 DOI:10.13001/ela.2023.7851

P. Danchev, E. García, M. Gómez Lozano

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引用次数: 0

摘要

对于任意$n\ge 2$和固定$k\ge 1$，我们给出了矩阵环$\mathbb{M}_n(\mathbb{F})$中的任意非零方阵在任意域$\mathbb{F}$上写成可逆矩阵$U$与n ^k=0$的幂零矩阵$n $的和的充要条件。

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Decompositions of matrices into a sum of invertible matrices and matrices of fixed nilpotence

For any $n\ge 2$ and fixed $k\ge 1$, we give necessary and sufficient conditions for an arbitrary nonzero square matrix in the matrix ring $\mathbb{M}_n(\mathbb{F})$ to be written as a sum of an invertible matrix $U$ and a nilpotent matrix $N$ with $N^k=0$ over an arbitrary field $\mathbb{F}$.

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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.