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