广义二次矩阵表达式的唯一性

IF 1 4区数学 Q1 MATHEMATICS Open Mathematics Pub Date : 2024-03-20 DOI:10.1515/math-2023-0186

Meixiang Chen, Zhongpeng Yang, Qinghua Chen

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引用次数: 0

摘要

通过数字实例证明，广义二次矩阵的表达式 A 2 = α A + β P {A}^{2}=\alpha A+\beta P 并不是唯一的。然后证明广义二次矩阵表达式的唯一性不仅与 A A 的性质有关，还与 P P 的秩有关。此外，还得到了广义二次矩阵表达式唯一性的充分条件和必要条件。最后，还给出了关于广义二次矩阵的一些相关讨论。

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The uniqueness of expression for generalized quadratic matrices

It is shown that the expression as

A 2 = α A + β P

{A}^{2}=\alpha A+\beta P

for generalized quadratic matrices is not unique by numerical examples. Then it is proven that the uniqueness of expression for generalized quadratic matrices is concerned not only with the properties of

but also with the rank of

. Furthermore, the sufficient and necessary conditions for the uniqueness of generalized quadratic matrices’expression are obtained. Finally, some related discussions about generalized quadratic matrices are also given.

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来源期刊

Open Mathematics MATHEMATICS-

CiteScore

2.40

自引率

5.90%

发文量

审稿时长

16 weeks

期刊介绍： Open Mathematics - formerly Central European Journal of Mathematics Open Mathematics is a fully peer-reviewed, open access, electronic journal that publishes significant, original and relevant works in all areas of mathematics. The journal provides the readers with free, instant, and permanent access to all content worldwide; and the authors with extensive promotion of published articles, long-time preservation, language-correction services, no space constraints and immediate publication. Open Mathematics is listed in Thomson Reuters - Current Contents/Physical, Chemical and Earth Sciences. Our standard policy requires each paper to be reviewed by at least two Referees and the peer-review process is single-blind. Aims and Scope The journal aims at presenting high-impact and relevant research on topics across the full span of mathematics. Coverage includes: