Commutation matrices and commutation tensors. Issue 9 (1st September 2020)

• Record Type: Journal Article
• Authors: Xu, Changqing; He, Lingling; Lin, Zerong
• Is Part Of: Linear & multilinear algebra. Volume 68:Issue 9(2020)
• Page Start: 1721
• Page End: 1742
• Publication Date: 2020-09-01
• Subjects: J. Y. Shao; Commutation matrix -- commutation tensor -- linear preserver -- determinant -- transpose; 15A69 -- 15A86; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2018.1556242
• Languages: English
• ISSNs: 0308-1087

Abstract

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.