交换矩阵和交换张量
Commutation matrices and Commutation tensors
摘要：
交换矩阵最早是由Murnaghan在1938年作为转置矩阵引入统计学的。本文首先研究了将矩阵变换成其转置矩阵的交换矩阵。然后将交换矩阵的概念推广到交换张量，并利用交换张量统一了Marcus在1971年的经典结果--矩阵秩的线性乘积的两个公式.
英文摘要：
The commutation matrix was first introduced in statistics as a transposition matrix by Murnaghan in 1938. In this paper, we first investigate the commutation matrix which is employed to transform a matrix into its transpose. We then extend the concept of the commutation matrix to commutation tensor and use the commutation tensor to achieve the unification of the two formulae of the linear preserver of the matrix rank, a classical result of Marcus in 1971.
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