Matrices: Peculiar Determinant Property
DOI:
https://doi.org/10.5281/zenodo.11266018Keywords:
Matrices, Determinant, DivisibilityAbstract
This paper provides a review of the theory surrounding matrices and determinants. While modern mathematics treats matrices and determinants as interconnected concepts, historically, determinants were recognized long before matrices were formally defined. The term "determinant" emerged in mathematical discourse over two centuries prior to the formal introduction of matrices. In this paper, we present a noteworthy property of square matrices: the divisibility of determinants. We show that for each row, where each row represents one number, are all divisible by some number d, then, in turn, the determinant of the matrix will also be divisible by the same number d. The findings of this study are of great importance as matrices with special additive determinant properties can be used for graph applications together with network analysis.
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