A Generalization of Chio’s Condensation Method
Abstract
The Chio condensation method is a method to compute the determinant of a matrix A where by reducing the order of the matrix to a matrix. In this paper, we will generalize the condition where can be equal to zero. To compute the determinant, we can choose any element of matrix A that is not equal to zero as a pivot element.
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References
H. Anton and C. Rorres, Elementary Linear Algebra: Applications Version, 10th edition. United States : John Wiley & Sons, 2010.
H. Eves, Elementary Matrix Theory. United States of America : Dover Publications, Inc, 1966.
F. CHIÒ, M´emoire sur les Fonctions Connues Sous Le Nom De R´esultantes Ou De D´eterminans. Torino: Edité par Pons, 1853.
Rev. C. L. Dodgson, “Condensation of Determinants, being a new and brief Method for computing their arithmetical values,” Proceedings of the Royal Society of London, vol. 15, pp. 150–155, 1867.
K. Habgood and I. Arel, “A condensation-based application of Cramer’s rule for solving large-scale linear systems,” Journal of Discrete Algorithms, vol. 10, no. 1, pp. 98–109, Jan. 2012, doi: 10.1016/j.jda.2011.06.007.
A. Salihu and Q. Gjonbalaj, “New Method to Compute the Determinant of a 4x4 Matrix,” 2009. [Online]. Available: https://www.researchgate.net/publication/275580759
A. Salihu and F. Marevci, “Chio’s-like method for calculating the rectangular (non-square) determinants: Computer algorithm interpretation and comparison,” European Journal of Pure and Applied Mathematics, vol. 14, no. 2, pp. 431–450, 2021, doi: 10.29020/NYBG.EJPAM.V14I2.3920.
D. Grinberg, K. Karnik, and A. Zhang, “From Chio Pivotal Condensation to the Matrix-Tree theorem,” 2016.
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