矩阵半张量积及换位矩阵的几点注解
SOME NOTES ON SEMI-TENSOR PRODUCT OF MATRICES AND SWAP MATRIX
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
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 .
张量积 /
换位矩阵 /
半张量积 /
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