# ON THE COMMUTATION MATRIX

• 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
Keywords: Commutation Matrix, Vec Matrix, Vec Transpose Matrix

### 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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Published
2023-12-19
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.
Section
Articles