| Schur补矩阵秩的不等式性质 |
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| 引用本文： | 段复建 狄勇婧. Schur补矩阵秩的不等式性质[J]. 长春大学学报, 2014, 0(2): 171-174 |
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| 作者姓名： | 段复建 狄勇婧 |
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| 作者单位： | 桂林电子科技大学数学与计算科学学院,广西桂林541004 |
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| 基金项目： | 广西自然基金（2011GXNSFA018138） |
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| 摘 要： | 矩阵的秩是矩阵的主要特征之一,而矩阵的Schur补又是处理大规模矩阵的主要途径。本文在研究了实数与矩阵乘积的Schur补、共轭转置矩阵的Schur补与矩阵秩的等式关系之后,又给出了幂矩阵与Schur补矩阵之间的秩的不等式性质,从而为处理大规模的矩阵计算提供了理论支撑。
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| 关 键 词： | 矩阵的秩 Schur补矩阵 矩阵乘积 初等变换 |
Inequality Properties of the Rank of Schur Complement Matrix |
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| DUAN Fu-jian,DI Yong-jing. Inequality Properties of the Rank of Schur Complement Matrix[J]. Journal of Changchun University, 2014, 0(2): 171-174 |
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| Authors: | DUAN Fu-jian DI Yong-jing |
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| Affiliation: | (School of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin 541004, China) |
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| Abstract: | The rank of matrix is one of the major characteristics, and Schur complement is the main way to deal with large-scale ma- trix. This paper, based on studying the relations between real number and Schur complement of matrix product, as well as Schur com- plement of conjugated transpose matrix and the equality of the rank of matrix, gives the inequality properties of rank between power ma- trix and Schur complement matrix, which provides a theoretical support for dealing with large-scale matrix caiculation. |
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| Keywords: | rank of matrix Schur complement matrix multiplication elementary transformation |
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