| 有限维中心代数上矩阵方程组的广对称解与斜广对称解 |
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| 引用本文： | 王卿文,李尚志. 有限维中心代数上矩阵方程组的广对称解与斜广对称解[J]. 数学学报, 2004, 47(1): 27-34. DOI: cnki:ISSN:0583-1431.0.2004-01-003 |
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| 作者姓名： | 王卿文 李尚志 |
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| 作者单位： | 1. 上海大学数学系,上海,200436
2. 中国科学技术大学数学系,合肥,230026 |
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| 基金项目： | 国家自然科学基金资助项目 |
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| 摘 要： | 设Ω是一个具有对合反自同构的有限维中心代数且charΩ≠2.本文在Ω上定义了广对称矩阵和斜广对称矩阵,在Ω[λ]上考虑了三个矩阵方程组,分别给出了其有广对称解和斜广对称的充要条件.作为特例,得到了某些矩阵方程相应的结果.
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| 关 键 词： | 广对称矩阵 斜广对称矩阵 矩阵方程组 |
| 文章编号： | 0583-1431(2004)01-0027-08 |
Persymmetric and Perskewsymmetric Solutions to Sets of Matrix Equations over a Finite Central Algebra |
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| Qing Wen WANG. Persymmetric and Perskewsymmetric Solutions to Sets of Matrix Equations over a Finite Central Algebra[J]. Acta Mathematica Sinica, 2004, 47(1): 27-34. DOI: cnki:ISSN:0583-1431.0.2004-01-003 |
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| Authors: | Qing Wen WANG |
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| Affiliation: | Qing Wen WANG (Department of Mathematics, Shanghai University, Shanghai 200436, P. R. China)Shang Zhi LI(Department of Mathematics, University of Science and Technology of China, Hefei 230026, P. R. China) |
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| Abstract: | Let Ω be a finite dimensional central algebra with an involutorial antiauto-morphism and char Ω≠2. Persymmetric and perskewsymmetric matrices over Ω are defined. Three systems of matrix equations over Ω[λ] are considered. Necessary and sufficient conditions for the existences of constant solutions with persymmmetric and perskewsymmetric constraints to the systems mentioned above are given. As a special case, some results dealing with the corresponding matrix equations are also presented. |
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| Keywords: | Persymmetric matrix Perskewsymmetric matrix System of linear equations |
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