广义Hadamard延拓矩阵的奇异值分解

聂祥荣,郭爱丽,武玲玲

doi:10.13718/j.cnki.xsxb.2018.08.001

西南师范大学学报(自然科学版)

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广义Hadamard延拓矩阵的奇异值分解

聂祥荣,郭爱丽,武玲玲. 广义Hadamard延拓矩阵的奇异值分解[J]. 西南师范大学学报(自然科学版), 2018, 43(8): 1-5. doi: 10.13718/j.cnki.xsxb.2018.08.001

引用本文:

聂祥荣,郭爱丽,武玲玲. 广义Hadamard延拓矩阵的奇异值分解[J]. 西南师范大学学报(自然科学版), 2018, 43(8): 1-5. doi: 10.13718/j.cnki.xsxb.2018.08.001

NIE Xiang-rong, GUO Ai-li, WU Ling-ling. Singular Value Decomposition for Generalized Hadamard-Extended Matrix[J]. Journal of Southwest China Normal University(Natural Science Edition), 2018, 43(8): 1-5. doi: 10.13718/j.cnki.xsxb.2018.08.001

Citation:

NIE Xiang-rong, GUO Ai-li, WU Ling-ling. Singular Value Decomposition for Generalized Hadamard-Extended Matrix[J]. Journal of Southwest China Normal University(Natural Science Edition), 2018, 43(8): 1-5. doi: 10.13718/j.cnki.xsxb.2018.08.001

广义Hadamard延拓矩阵的奇异值分解

聂祥荣,郭爱丽,武玲玲

贵州工程应用技术学院数学系, 贵州毕节 551700

Singular Value Decomposition for Generalized Hadamard-Extended Matrix

NIE Xiang-rong, GUO Ai-li, WU Ling-ling

Department of Mathematics, Guizhou University of Engineering Science, Bijie Guizhou 551700, China

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和√kn+1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.
- 延拓矩阵 /
- 母矩阵 /
- Hadamard矩阵 /
- 奇异值分解 /
- Moore-Penrose逆
Abstract: 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 and √kn+1 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.
- extended matrix /
- original matrix /
- Hadamard matrix /
- singular value decomposition /
- Moore-Penrose inverse .

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广义Hadamard延拓矩阵的奇异值分解

聂祥荣,郭爱丽,武玲玲

贵州工程应用技术学院数学系, 贵州毕节 551700

收稿日期: 2017-11-14

关键词:

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和√kn+1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.

English Abstract

Singular Value Decomposition for Generalized Hadamard-Extended Matrix

贵州工程应用技术学院数学系, 贵州毕节 551700

Received Date: 2017-11-14

Keywords:

Abstract: 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 and √kn+1 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.