Geodesic
Alternative construction of the determinant theory
Trudy Instituta matematiki, Tome 32 (2024) no. 2, pp. 93-96

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We establish in a direct way, without involving the sigh function of permutations and matrice reducing to echelon form, the equivalence of the expansion of determinant along any row and any column. On base of this the rest of the theory of determinants is significantly simplified: determinant multiplicativity, the generalized Laplace expansion and Cauchy–Binet formula and so on.
Keywords: the equality theorem, the multiplicative property of determinants, the generalized Laplace expansion and Cauchy–Binet formula. 
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S. M. Ageev; H. S. Ageeva. Alternative construction of the determinant theory. Trudy Instituta matematiki, Tome 32 (2024) no. 2, pp. 93-96. http://geodesic.mathdoc.fr/item/TIMB_2024_32_2_a8/