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.
Published Version
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