| 任意体上的双矩阵分解与矩阵方程 |
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| 引用本文： | 王卿文. 任意体上的双矩阵分解与矩阵方程[J]. 数学学报, 1996, 39(3): 396-403. DOI: cnki:ISSN:05831431.0.1996-03-014 |
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| 作者姓名： | 王卿文 |
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| 作者单位： | 山东昌潍师专数学系 |
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| 摘 要： | 本文给出了任意体上具有相同行数或相同列数的双矩阵分解定理；利用此定理，给出了任意体上的矩阵方程ＡＸＢ＋ＣＹＤ＝Ｅ及［Ａ１ＸＢ１，Ａ２ＸＢ２］＝［Ｅ１；Ｅ２］有解的充要条件及其一般解的表达式．
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| 关 键 词： | 体，矩阵分解，矩阵方程 |
| 收稿时间： | 1994-09-14 |
| 修稿时间： | 1995-05-15 |
The Decomposition of Pairwise Matrices and Matrix Equations over an Arbitrary Skew Field |
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| Wang QingWen. The Decomposition of Pairwise Matrices and Matrix Equations over an Arbitrary Skew Field[J]. Acta Mathematica Sinica, 1996, 39(3): 396-403. DOI: cnki:ISSN:05831431.0.1996-03-014 |
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| Authors: | Wang QingWen |
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| Affiliation: | Wang QingWen(Department of Mathematics, Changwei Teachers College, Weifang 261043, China) |
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| Abstract: | A decomposition of pairwise matrices over an arbitrary skew field F with same numbers of rows or colunms is presented. New necessaryand sufficiellt conditions for the consistency of the matrix equations (i) AXB CYD = E and (ii) [A1XB1, A2XB2] = [E1, E2] over F are derived and their general solutions are also given by using the decomposition theorem. |
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| Keywords: | skew field matrix decomposition matrix equation |
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