<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml"><p>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</p></abstract>

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

Basic Properties of Determinants of Square Matrices over a Field<sup>1</sup>

Institute of Computer Science, University of Białystok, Poland

Formalized Mathematics

Basic Properties of Determinants of Square Matrices over a Field

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...

Basic Properties of Determinants of Square Matrices over a Field¹

Online veröffentlicht: 13. Juni 2008

Seitenbereich: 17 - 25

DOI: https://doi.org/10.2478/v10037-007-0003-x

This content is open access.

Basic Properties of Determinants of Square Matrices over a Field1

Online veröffentlicht: 13. Juni 2008

Seitenbereich: 17 - 25

DOI: https://doi.org/10.2478/v10037-007-0003-x

This content is open access.

Basic Properties of Determinants of Square Matrices over a Field¹