Schur补矩阵秩的不等式性质  

Inequality Properties of the Rank of Schur Complement Matrix

作　　者：段复建[1] 狄勇婧[1] 

机构地区：[1]桂林电子科技大学数学与计算科学学院,广西桂林541004

出　　处：《长春大学学报》2014年第2期171-174,共4页Journal of Changchun University

基　　金：广西自然基金(2011GXNSFA018138)

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。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.

关 键 词：矩阵的秩 Schur补矩阵 矩阵乘积 初等变换 

分 类 号：O151.21[理学—数学]