Commutation matrices and Commutation tensors
Combinatorics
2018-08-17 v2
Abstract
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.
Cite
@article{arxiv.1808.04561,
title = {Commutation matrices and Commutation tensors},
author = {Changqing Xu},
journal= {arXiv preprint arXiv:1808.04561},
year = {2018}
}
Comments
23 pages, 0 figure, part of this work was presented at the 2018 international conference on Matrices and operators (MAO2018) in Shanghai