Alternative construction of the determinant theory
Abstract
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
About the Authors
S. M. Ageev
Belarusian State University
Belarus
Belarus
Minsk
H. S. Ageeva
Belarusian State University
Belarus
Belarus
Minsk
References
1. Botha J. D. Alternative proofs of the rational canonical form theorem. Int. J. Math. Educ. Sci. Technol., 1994, vol. 25, no. 5, pp. 745–749.
2. Filippov A. F. A short proof of the theorem on the reduction of a matrix to Jordan form. Mosc. Univ. Math. Bull., 1971, vol. 26, no. 1–2, pp. 70–71.
Review
For citations:
Ageev S.M., Ageeva H.S. Alternative construction of the determinant theory. Proceedings of the Institute of Mathematics of the NAS of Belarus. 2024;32(2):93-96. (In Russ.)
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