矩阵半张量积及换位矩阵的几点注解

王元华,刘挺,程代展

系统科学与数学 ›› 2016, Vol. 36 ›› Issue (9) : 1367-1375.

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PDF(358 KB)
系统科学与数学 ›› 2016, Vol. 36 ›› Issue (9) : 1367-1375. DOI: 10.12341/jssms12892
论文

矩阵半张量积及换位矩阵的几点注解

    王元华1,刘挺2,程代展3
作者信息 +

SOME NOTES ON SEMI-TENSOR PRODUCT OF MATRICES AND SWAP MATRIX

    WANG Yuanhua1,LIU Ting2,Cheng Daizhan3
Author information +
文章历史 +

摘要

矩阵半张量积是一种新的矩阵乘法, 它将普通矩阵乘法推广到任意两个矩阵, 同时又保留了普通矩阵乘法的主要性质. 换位矩阵使矩阵乘法具有一定的交换性质, 从而使得矩阵半张量积 更为有效. 文章首先讨论了矩阵半张量积与矩阵张量积之间的关系. 然后讨论换位矩阵在矩阵张量积中的应用. 最后, 将换位矩阵推广到对应于任意置换σσ-置换矩阵.

Abstract

Semi-tensor product of matrices is a new matrix product, which is a generalization of conventional matrix product for two arbitrary matrices. Meanwhile, it maintains almost all fundamental properties of conventional matrix product. Swap matrix provides certain commutative property to semi-tensor product of matrices, which makes it more effective. This paper discusses the relationship between the semi-tensor product and Kronecker product of matrices first. Then the application of swap matrix to the Kronecker product of matrices is considered. Finally, the swap matrix is extended to the -permutation matrix, which can realize factor permutation for an arbitrary permutation .

关键词

张量积 / 换位矩阵 / 半张量积 / σ-置换矩阵.

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王元华 , 刘挺 , 程代展. 矩阵半张量积及换位矩阵的几点注解. 系统科学与数学, 2016, 36(9): 1367-1375. https://doi.org/10.12341/jssms12892
WANG Yuanhua , LIU Ting , Cheng Daizhan. SOME NOTES ON SEMI-TENSOR PRODUCT OF MATRICES AND SWAP MATRIX. Journal of Systems Science and Mathematical Sciences, 2016, 36(9): 1367-1375 https://doi.org/10.12341/jssms12892
中图分类号: 15A69   
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