Preprint Concept Paper Version 1 Preserved in Portico This version is not peer-reviewed

Computation of Matrix Determinants by Cross-Multiplication: A Rethinking of Dodgson’s Condensation and Reduction by Elementary Row Operations Methods

Version 1 : Received: 25 June 2023 / Approved: 26 June 2023 / Online: 27 June 2023 (07:57:21 CEST)

A peer-reviewed article of this Preprint also exists.

Protacio, J.V. Computation of Matrix Determinants by Cross-Multiplication: A Rethinking of Dodgson’s Condensation and Reduction by Elementary Row Operations Methods. Symmetry 2023, 15, 1456. Protacio, J.V. Computation of Matrix Determinants by Cross-Multiplication: A Rethinking of Dodgson’s Condensation and Reduction by Elementary Row Operations Methods. Symmetry 2023, 15, 1456.

Abstract

We formulate a more straightforward, symmetry-based techniques in manually computing the determinant of any n×n matrix by revisiting Dodgson’s condensation method and strategically applying elementary row operations and the definition and properties of determinants. The result yields a more simplified mnemonical algorithm than the usual reduction by elementary row operations and co-factor expansion and with minimal terminal divisions performed compared to Dodgson’s internal divisions.

Keywords

matrix determinant; Dodgson’s condensation, cross-multiplication

Subject

Computer Science and Mathematics, Mathematics

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