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.
Subject
Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)
Reference19 articles.
1. Eves, H. (1990). An Introduction to the History of Mathematics, Saunders College Publishing.
2. Condensation of determinants, being a new and brief method for computing their arithmetical values;Dodgson;Proc. R. Soc. Lond.,1867
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.].