| 向量交换矩阵一种新的定义及应用 |
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| 引用本文： | 张华民,殷红彩.向量交换矩阵一种新的定义及应用[J].纯粹数学与应用数学,2013(3):246-254. |
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| 作者姓名： | 张华民 殷红彩 |
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| 作者单位： | [1]蚌埠学院数理系,安徽蚌埠233030 [2]江南大学控制科学与工程研究中心,江苏无锡214122 [3]安徽财经大学管理科学与工程学院,安徽蚌埠233000 |
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| 基金项目： | 国家自然科学基金（60973043）;111引智计划（B12018）;蚌埠学院自然科学基金（2011ZR17）;安徽高等学校省级自然科学研究项目fKJ2013A183）. |
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| 摘 要： | 利用单位矩阵和基本向量给出了向量交换矩阵的一种较以往表述简单的新的定义.基于新的定义证明了向量交换矩阵的性质.给出了新定义与原有定义的等价性的证明.最后给出了矩阵克罗内克积奇异值的一个新的结论.
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| 关 键 词： | 克罗内克积 向量交换矩阵 向量化算子 奇异值 |
A new definition of vec-permutation matrix and its applications |
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| Zhang Huamin,Yin Hongcai.A new definition of vec-permutation matrix and its applications[J].Pure and Applied Mathematics,2013(3):246-254. |
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| Authors: | Zhang Huamin Yin Hongcai |
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| Institution: | 1. Department of Mathematics and Physics, Bengbu College, Bengbu 233030, China; 2. Control Science and Engineering Research Center, Jiangnan University, Wuxi 214122, China; 3. School of Management Science and Engineering, Anhui University of Finance ＆ Economics, Bengbu 233000, China) |
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| Abstract: | By using the Kronecker product of the identity matrix and the fundamental vector, a new definition of vec-permutation matrix is presented, which is simpler than the original one. Based on the new definition, the properties of the vec-permutation matrix are discussed. The proof of the equivalence between the new definition and the original one is given. At last, a new result on the singular values of Kroneker products of several matricesis established. |
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| Keywords: | Kronecker product vec-permutation matrix vector operator singular values |
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