| 关于矩阵秩等式研究的注记 |
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| 引用本文： | 杨忠鹏,陈梅香.关于矩阵秩等式研究的注记[J].莆田学院学报,2008,15(5). |
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| 作者姓名： | 杨忠鹏 陈梅香 |
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| 作者单位： | 莆田学院,数学与应用数学系,福建,莆田,351100 |
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| 基金项目： | 福建省自然科学基金，莆田学院校科研和教改项目，福建省本科精品课程--高等代数 |
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| 摘 要： | 最近一些文献应用自反广义逆和广义Schur补得到了一些重要的矩阵秩的恒等式。对这些结果,给出了只用分块初等变换的简单证法;作为应用对k(k=2,3,4)幂等矩阵的秩等式作进一步讨论,还给出了打洞技巧在求秩上应用的例子。
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| 关 键 词： | 矩阵秩 分块矩阵 分块初等变换 k幂等矩阵 打洞技巧 |
Some Notes on the Rank Identity of Matrix |
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| YANG Zhong-peng,CHEN Mei-xiang.Some Notes on the Rank Identity of Matrix[J].journal of putian university,2008,15(5). |
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| Authors: | YANG Zhong-peng CHEN Mei-xiang |
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| Institution: | YANG Zhong-peng,CHEN Mei-xiang ( Mathematics & Applied Mathematics Department,Putian University,Putain Fujian 351100,China ) |
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| Abstract: | Recently, severval rank identities of a matrix are obtained by using reflexive generalized inverse and general Schur complement in the literature. For these results, a simple proof is presented by only using the elementary transformation of block matrix . As an application, rank identities of k-idempotent matrix are studied further, where k = 2, 3, 4. Meanwhile, some examples of the application of burrow technique to compute rank of a matrix are given. |
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| Keywords: | rank of matrix block matrix elementary transformation k-idempotent matrix technique of burrow |
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