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Vol 17 No 4 (2023): BAREKENG: Journal of Mathematics and Its Applications
Articles

ON THE COMMUTATION MATRIX

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  • Yanita Yanita,
  • Lyra Yulianti
Yanita Yanita
Department of Mathematics and Data Science, Faculty of Mathematics and Natural Science, Andalas University
Lyra Yulianti
Department of Mathematics and Data Science, Faculty of Mathematics and Natural Science, Andalas University
DOI: https://doi.org/10.30598/barekengvol17iss4pp1997-2010
Published December 19, 2023
Keywords
  • Commutation Matrix,
  • Vec Matrix,
  • Vec Transpose Matrix
How to Cite
[1]
Y. Yanita and L. Yulianti, “ON THE COMMUTATION MATRIX”, BAREKENG: J. Math. & App., vol. 17, no. 4, pp. 1997-2010, Dec. 2023.

Copyright (c) 2023 Yanita Yanita, Lyra Yulianti

Creative Commons License

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Abstract

The commutation matrix is a matrix that transforms any vec matrix , to vec transpose . In this article, three definitions of the commutation matrix are presented in different ways. It is shown that these three definitions are equivalent.  Proof of the equivalent uses the properties in the Kronecker product on the matrix.  We also gave the example of the commutation matrix using three ways as Moreover, in this study, we investigate the  properties of the commutation matrix related to its transpose and the relation between the vec matrix and the vec transpose matrix using the commutation matrix. We have that the transpose and the inverse of the commutation matrix is its transpose.

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