Cullis-Radić determinant of a rectangular matrix which has a number of identical columns

Abstract

In this paper we present how identical columns affect the Cullis-Radić determinant of an \(m\times n\) matrix, where \(m\leq n\).

Some 3D-Determinant Properties for Calculating of Cubic-Matrix of Order 2 and Order 3

“…In the paper [2], we have defined the concept of determinant for cubic-matrix of order 2 and order 3, and we have prove some basic properties for calculating this determinants. This idea for developing this concept, it came simply from the determinant of 2D square matrices [19][20][21][24][25][26]29], as well as determinant of rectangular matrices [3,[15][16][17][18][30][31][32][33]. In paper [1] we have prove that the Laplace expansion method is valid for calculating the determinant of cubic-matrix for orders 2 and 3.…”

Some 3D-Determinant Properties for Calculating of Cubic-Matrix of Order 2 and Order 3

“…This idea for developing this concept, it came simply from the determinant of 2D square matrices (Salihu et.al., 2021;Salihu et al, 2019b;Salihu, 2018;Artin, 1991;Bretscher 2005, Schneide et.al. 1973, as well as determinant of rectangular matrices (Salihu et al, 2022a, Salihu et al, 2023b, Salihu et al, 2022b, Salihu et al, 2022cSalihu et al, 2019a;Amiri et al, 2010;Radic, 1966;Radic, 2005;Makarewicz et al, 2014).…”