| 关于分块矩阵及矩阵和的列空间方程的研究 |
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| 引用本文： | 程士珍,田永革. 关于分块矩阵及矩阵和的列空间方程的研究[J]. 厦门大学学报(自然科学版), 2004, 43(2): 152-154 |
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| 作者姓名： | 程士珍 田永革 |
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| 作者单位： | 1. 天津工业大学理学院数学系,天津300160
2. 加拿大皇后大学数学与统计系,安大略,加拿大,K7L 3 N6 |
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| 基金项目： | 世行贷款21世纪初高等教育教学改革项目(128A01032)资助 |
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| 摘 要： | 给出了一个将分块矩阵的列空间方程简化成分块矩阵的秩方程的充分必要条件.同时利用著名的Frobenius秩不等式,给出将矩阵和的列空间方程简化成行分块矩阵的列空间方程的一个条件,并得出相应的一些推论.
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| 关 键 词： | 分块矩阵 列空间 秩 Moore-Penrose逆 |
| 文章编号： | 0438-0479(2004)02-0152-03 |
| 修稿时间： | 2003-04-06 |
A Note on Range Equalities for Block Matrices and Sums of Matrices |
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| CHENG Shi-zhen,TIAN Yong-ge. A Note on Range Equalities for Block Matrices and Sums of Matrices[J]. Journal of Xiamen University(Natural Science), 2004, 43(2): 152-154 |
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| Authors: | CHENG Shi-zhen TIAN Yong-ge |
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| Affiliation: | CHENG Shi-zhen~1,TIAN Yong-ge~2 |
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| Abstract: | The authors give necessary and sufficient conditions such that some range equalities for block matrices which can be used to simplify ranks of block matrices. Meantime we can derive a condition of some range equalities for sums of matrices that can be used to simplify range equalities of row block matrices by the well-known Frobenius rank inequality. As application, we also have the several corollaries from these. |
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| Keywords: | matrix range of matrix rank of matrix block matrix Moore-Penrose inverse of matrix |
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