Basic Properties of Determinants of Square Matrices over a Field 1

Karol Pąk

Formalized Mathematics, Tome 15 (2007), p. 17-25 / Harvested from The Polish Digital Mathematics Library

Résumé

In this paper I present basic properties of the determinant of square matrices over a field and selected properties of the sign of a permutation. First, I define the sign of a permutation by the requirement [...] where p is any fixed permutation of a set with n elements. I prove that the sign of a product of two permutations is the same as the product of their signs and show the relation between signs and parity of permutations. Then I consider the determinant of a linear combination of lines, the determinant of a matrix with permutated lines and the determinant of a matrix with a repeated line. Finally, at the end I prove that the determinant of a product of two square matrices is equal to the product of their determinants.MML identifier: MATRIX11, version: 7.8.04 4.81.962

Détail

Publié le : 2007-01-01
EUDML-ID : urn:eudml:doc:267525

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