由两个幂等矩阵生成的代数的综合分类

IF 1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2024-11-07 DOI:10.1016/j.laa.2024.11.005

Rounak Biswas, Falguni Roy

引用次数: 0

摘要

对于两个幂等矩阵 P,Q∈Cn×n, 让 alg(In,P,Q) 表示 Cn×n 中包含 P,Q 和同一矩阵 In 的最小子代数。本文在不对 P 和 Q 施加任何限制的情况下，对 alg(In,P,Q) 进行了完整的分类。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Comprehensive classification of the algebra generated by two idempotent matrices

For two idempotent matrix

P, Q \in C^{n \times n}

, let alg

(I_{n}, P, Q)

denote the smallest subalgebra of

C^{n \times n}

that contains

P, Q

and the identity matrix

I_{n}

. This paper provides a complete classification of alg

(I_{n}, P, Q)

without imposing any restrictions on P and Q. As a result of this classification, the issue of group invertibility within alg

(I_{n}, P, Q)

is fully resolved.

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来源期刊

Linear Algebra and its Applications 数学-应用数学

CiteScore

2.20

自引率

9.10%

发文量

333

审稿时长

13.8 months

期刊介绍： Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.