Generalization of Dodgson’s condensation method for calculating determinant of rectangular matrices

Salihu, Armend; Snopce, Halil; Ajdari, Jaumin; Luma, Artan

doi:10.1109/icecet55527.2022.9873054

Cited by 4 publications

(2 citation statements)

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“…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.…”

Section: Introductionmentioning

confidence: 99%

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

Salihu¹,

Zaka²

2023

Preprint

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In this paper we have studied some properties for determinant-calculating for cubic-matrix of order 2 and order 3. These properties are analogous to some properties for determinants of square matrix we have proved and noted that these properties also are applicable (or not in some details) on this concept for cubic-matrix of orders 2 and 3. All results in this paper, are presented in detail during the theorem proofs.

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Section: Introductionmentioning

confidence: 99%

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

Salihu¹,

Zaka²

2023

Preprint

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“…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).…”

Section: Introductionmentioning

confidence: 99%

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

SALIHU,

ZAKA

2023

EPSTEM

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In this paper, as a continuation of our work on the determinant of cubic matrices, we have studied some properties of calculation of the determinant of cubic matrices for the cubic matrix of the order 2×2, as well as the order 3×3. Like properties of square determinants, these properties are analogous to some properties for determinants of the square matrix we have proved and noted that these properties also are applicable (or not in some details) to this concept for the determinant of the cubic matrix of orders 2×2 and order 3×3. All properties that have been proved in this paper, are proved for each case for orders 2×2 and order 3×3, by including all elements of the matrix, as well as all horizontal plans, horizontal layers, and vertical layers. All results in this paper, are presented in detail during the theorem proofs.

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Implementation on a Parallel Environment of Generalized/Modified Dodgson’s Method for Rectangular Determinants Calculation

Salihu

Snopce

Ajdari

et al. 2022

2022 32nd International Conference on Computer Theory and Applications (ICCTA)

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Generalization of Dodgson’s condensation method for calculating determinant of rectangular matrices

Cited by 4 publications

References 4 publications

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

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

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

Implementation on a Parallel Environment of Generalized/Modified Dodgson’s Method for Rectangular Determinants Calculation

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