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.
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)
关键词
矩阵的秩
Schur补矩阵
矩阵乘积
初等变换
rank of matrix
Schur complement
matrix multiplication
elementary transformation
