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Vol 19 No 1 (2025): BAREKENG: Journal of Mathematics and Its Application
Articles

A STUDY ON THE STRUCTURE OF MATRICES RELATED TO THE VECH*, VECP*, AND VEC OPERATORS

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  • Nurul Hidayah,
  • Yanita Yanita,
  • Admi Nazra
Nurul Hidayah
Department of Mathematics Education and Natural Science, Faculty of Teacher Training and Education, Universitas Jambi, Indonesia
Yanita Yanita
Department of Mathematics and Data Science, Faculty of Mathematics and Natural Sciences, Universitas Andalas, Indonesia
Admi Nazra
Department of Mathematics and Data Science, Faculty of Mathematics and Natural Sciences, Universitas Andalas, Indonesia
DOI: https://doi.org/10.30598/barekengvol19iss1pp259-270
Published January 13, 2025
Keywords
  • vec,
  • vech*,
  • vecp*,
  • Duplication Matrix,
  • Commutation Matrix
How to Cite
[1]
N. Hidayah, Y. Yanita, and A. Nazra, “A STUDY ON THE STRUCTURE OF MATRICES RELATED TO THE VECH*, VECP*, AND VEC OPERATORS”, BAREKENG: J. Math. & App., vol. 19, no. 1, pp. 259-270, Jan. 2025.

Copyright (c) 2025 Nurul Hidayah, Yanita Yanita, Admi Nazra

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

Abstract

The vec operator is an essential tool in matrix algebra that transforms a matrix into a column vector based on specific rules. This paper introduces two new operators, namely  and , which take the main diagonal and supra-diagonal elements of the matrix, respectively. In this paper, we obtain the general form of the matrix , which transform  to , with  as a matrix of size . In addition, we also develop the general forms of matrices and , which transform  into  and  into , with  as a symmetric matrix of size . This study also explores the properties and relationships between these matrices and their relevance to duplication and commutation matrices, providing deeper insights into the structure and operations of matrices.

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