# Basic Properties of Determinants of Square Matrices over a Field 1

Formalized Mathematics (2007)

- Volume: 15, Issue: 1, page 17-25
- ISSN: 1426-2630

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topKarol Pąk. " Basic Properties of Determinants of Square Matrices over a Field 1 ." Formalized Mathematics 15.1 (2007): 17-25. <http://eudml.org/doc/267525>.

@article{KarolPąk2007,

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},

author = {Karol Pąk},

journal = {Formalized Mathematics},

language = {eng},

number = {1},

pages = {17-25},

title = { Basic Properties of Determinants of Square Matrices over a Field 1 },

url = {http://eudml.org/doc/267525},

volume = {15},

year = {2007},

}

TY - JOUR

AU - Karol Pąk

TI - Basic Properties of Determinants of Square Matrices over a Field 1

JO - Formalized Mathematics

PY - 2007

VL - 15

IS - 1

SP - 17

EP - 25

AB - 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

LA - eng

UR - http://eudml.org/doc/267525

ER -

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