广义Hadamard延拓矩阵的奇异值分解  

Singular Value Decomposition for Generalized Hadamard-Extended Matrix

作　　者：聂祥荣 郭爱丽 武玲玲 NIE Xiang-rong;GUO Ai-li;WU Ling-ling(Department of Mathematics,Guizhou University of Engineering Science,Bilie Guizhou 551700,China)

机构地区：[1]贵州工程应用技术学院数学系,贵州毕节551700

出　　处：《西南师范大学学报（自然科学版）》2018年第8期1-5,共5页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：贵州省科学技术基金项目(LKB[2013]11);贵州省科学技术基金项目(LH[2014]7531);贵州省科技计划项目(黔科合平台人才[2017]5502);毕节市科学技术项目(毕科合字[2017]05)

摘　　要：定义广义行(列)Hadamard延拓矩阵的概念,分别建立广义行Hadamard延拓矩阵和广义列Hadamard延拓矩阵与母矩阵的奇异值和奇异向量之间的定量关系.对m×n阶母矩阵进行k次行和列延拓,所得延拓矩阵的奇异值分别是母矩阵奇异值的(km+1)(1/2)和(kn+1)(1/2)倍.作为应用,分别给出行和列Hadamard延拓矩阵的Moore-Penrose逆.最后举例验证所得结果.The row（column）generalized Hadamard-extended matrix is defined in this paper.Some quantitative correspondences of the singular values and singular vectors between the row and column generalized Hadamard-extended matrices and their original matrix are derived.For a m×n matrix,the singular values of the k-order row and k-order column extended matrices are proved to be equal to （km＋1）（1/2） and （kn＋1）（1/2） times of those of the original matrix,respectively.As applications,the formulas of Moore-Penrose inverses of the row and column generalized Hadamard-extended matrices are given,respectively.Furthermore,a numerical example is also presented to illustrate the results in this paper.

关 键 词：延拓矩阵 母矩阵 HADAMARD矩阵 奇异值分解 MOORE-PENROSE逆 

分 类 号：O151.21[理学—数学]