| 广义二次矩阵与其幂等矩阵线性组合幂等性的非平凡解 |
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| 引用本文： | 陈梅香,叶铃滢,杨忠鹏. 广义二次矩阵与其幂等矩阵线性组合幂等性的非平凡解[J]. 吉林大学学报(理学版), 2021, 59(2): 221-228. DOI: 10.13413/j.cnki.jdxblxb.2020255 |
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| 作者姓名： | 陈梅香 叶铃滢 杨忠鹏 |
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| 作者单位： | 1. 莆田学院 数学与金融学院, 福建 莆田 351100; 2. 福建师范大学 数学与信息学院, 福州 350007 |
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| 基金项目： | 国家自然科学基金;福建省自然科学基金 |
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| 摘 要： | 首先,用广义二次矩阵的基本性质,研究表示为A2=αA+βP的广义二次矩阵A与幂等矩阵P的线性组合ρA+σP为幂等的非平凡解(ρ,σ)的存在性,结果表明,当η2=4β+α2≠0时,ρA+σP有且仅有两个非平凡解,A可唯一地表示为这两个非平凡解生成的幂等矩阵的线性组合;其次,讨论当η2=4β+α2=0时ρA+σP非平凡解的...
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| 关 键 词： | 广义二次矩阵 幂等矩阵 幂零矩阵 线性组合 非平凡解 |
| 收稿时间： | 2020-08-31 |
Nontrivial Solutions of Idempotency of Linear Combinations of Generalized Quadratic Matrix and Its Idempotent Matrix |
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| CHEN Meixiang,YE Lingying,YANG Zhongpeng. Nontrivial Solutions of Idempotency of Linear Combinations of Generalized Quadratic Matrix and Its Idempotent Matrix[J]. Journal of Jilin University: Sci Ed, 2021, 59(2): 221-228. DOI: 10.13413/j.cnki.jdxblxb.2020255 |
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| Authors: | CHEN Meixiang YE Lingying YANG Zhongpeng |
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| Affiliation: | 1. School of Mathematics and Finance, Putian University, Putian 351100, Fujian Province, China;
2. College of Mathematics and Informatics, Fujian Normal University, Fuzhou 350007, China |
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| Abstract: | Firstly, by using the basic properties of generalized quadratic matrices, we studied the existence of the nontrivial solution (ρ,σ) for the linear combination ρA+σP of generalized quadratic matrix A and an idempotent matrix P expressed as A2=αA+βP. The results show that when η2=4β+α2≠0, ρA+σP has only two nontrivial solutions, and the matrix A can be uniquely expressed as a linear combination of idempotent matrix generated by these two nontrivial solutions. Secondly, we discussed the case for nontrivial solution of ρA+σP when η2=4β+α2=0. |
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| Keywords: | generalized quadratic matrix idempotent matrix nilpotent matrix linear combination nontrivial solution |
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