| 一类矩阵秩恒等式的证明 |
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| 引用本文： | 王廷明,黎伯堂.一类矩阵秩恒等式的证明[J].山东大学学报(理学版),2007,42(2):43-45. |
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| 作者姓名： | 王廷明 黎伯堂 |
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| 作者单位： | 1. 青岛大学,师范学院数学系,山东,青岛,266071
2. 山东大学,数学与系统科学学院,山东,济南,250100 |
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| 摘 要： | 利用矩阵的Jordan标准形，证明了当k1,k2,…kt满足与矩阵A的特征根有关的条件时，关于一类矩阵秩恒等式的猜想成立，并对相关的矩阵秩的恒等式进行了推广．
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| 关 键 词： | 矩阵 秩 特征根 |
| 文章编号： | 1671-9352（2007）02-0043-03 |
| 收稿时间： | 2006-05-25 |
| 修稿时间： | 2006-05-25 |
Proof of a class of matrix rank identities |
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| WANG Ting-ming,LI Bo-tang.Proof of a class of matrix rank identities[J].Journal of Shandong University,2007,42(2):43-45. |
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| Authors: | WANG Ting-ming LI Bo-tang |
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| Institution: | 1. Dept. Math., Teachers College of Qingdao Univ., Qingdao 266071, Shandong, China; 2. School of Math. and System Sci., Shandong Univ., Jinan 250100, Shandong, China |
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| Abstract: | By using Jordan canonical form of matrix,it is proved that when k1,k2,...kt satisfy the related conditions of characteristic root of matrix A,the speculation of a class of matrix rank identities is tenable.The identity of a related matrix rank is also extended. |
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| Keywords: | matrix rank characteristic root |
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