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

Author:

Protacio Judel Villas1ORCID

Affiliation:

1. College of Education, Arts and Sciences, Capiz State University, Roxas City 5802, Philippines

Abstract

We formulate a more straightforward, symmetry-based technique for manually computing the determinant of any n×n matrix by revisiting Dodgson’s condensation method, as well as strategically applying elementary row (column) operations and the definition and properties of determinants. The result yields a more streamlined algorithm that is generalized through formulas and employs a smaller number of operations and succeeding matrices than the existing methods.

Publisher

MDPI AG

Subject

Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)

Reference19 articles.

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3. Stinson, D.R. (2005). Cryptography. Discrete Mathematics and Its Applications, Chapman & Hall.

4. On the extension of Sarrus’ rule to n × n (n > 3) matrices: Development of new method for the computation of the determinant of 4 × 4 matrix;Sobamowo;Int. J. Eng. Math.,2016

5. Kolman, B., and Hill, D. (2014). Elementary Linear Algebra with Applications, Pearson Education Ltd.. [9th ed.].

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