矩阵和与幂的Schur补秩的性质  

Rank properties of Schur complement of matrices sum and power

作　　者：李春红 段复建[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：《桂林电子科技大学学报》2017年第4期337-340,共4页Journal of Guilin University of Electronic Technology

基　　金：国家自然科学基金(11461015)

摘　　要：为减小矩阵的规模,提高大型矩阵的计算效率,利用矩阵Schur补秩的理论知识和矩阵乘积的秩的不等式,分析了矩阵在加法和乘法下的Schur补的秩的性质,得到了矩阵幂运算的Schur补的秩与其子块幂的秩之间的等式关系、矩阵幂的秩与Schur补矩阵秩之间的不等式以及矩阵和的Schur补的秩的不等式。In order to reduce the scale of the matrix and improve the computational efficiency of the large matrix,rank properties of Schur complement of the matrix under the addition and multiplication are analysed by using the theoretical knowledge of the matrix Schur complement and the rank inequality of matrix product.The inequality between the rank of Schur complement and the rank of the subgroup power,the inequality between the rank of the matrix power and the rank of Schur complement matrix,and rank inequality of the matrices sum under Schur complement are obtained.

关 键 词：Schur补矩阵 矩阵的秩 分块矩阵 

分 类 号：O151.21[理学—数学]