Determinant of Some Matrices of Field Elements

Yatsuka Nakamura

Formalized Mathematics (2006)

  • Volume: 14, Issue: 1, page 1-5
  • ISSN: 1426-2630

Abstract

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Here, we present determinants of some square matrices of field elements. First, the determinat of 2 * 2 matrix is shown. Secondly, the determinants of zero matrix and unit matrix are shown, which are equal to 0 in the field and 1 in the field respectively. Thirdly, the determinant of diagonal matrix is shown, which is a product of all diagonal elements of the matrix. At the end, we prove that the determinant of a matrix is the same as the determinant of its transpose.

How to cite

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Yatsuka Nakamura. "Determinant of Some Matrices of Field Elements." Formalized Mathematics 14.1 (2006): 1-5. <http://eudml.org/doc/266969>.

@article{YatsukaNakamura2006,
abstract = {Here, we present determinants of some square matrices of field elements. First, the determinat of 2 * 2 matrix is shown. Secondly, the determinants of zero matrix and unit matrix are shown, which are equal to 0 in the field and 1 in the field respectively. Thirdly, the determinant of diagonal matrix is shown, which is a product of all diagonal elements of the matrix. At the end, we prove that the determinant of a matrix is the same as the determinant of its transpose.},
author = {Yatsuka Nakamura},
journal = {Formalized Mathematics},
language = {eng},
number = {1},
pages = {1-5},
title = {Determinant of Some Matrices of Field Elements},
url = {http://eudml.org/doc/266969},
volume = {14},
year = {2006},
}

TY - JOUR
AU - Yatsuka Nakamura
TI - Determinant of Some Matrices of Field Elements
JO - Formalized Mathematics
PY - 2006
VL - 14
IS - 1
SP - 1
EP - 5
AB - Here, we present determinants of some square matrices of field elements. First, the determinat of 2 * 2 matrix is shown. Secondly, the determinants of zero matrix and unit matrix are shown, which are equal to 0 in the field and 1 in the field respectively. Thirdly, the determinant of diagonal matrix is shown, which is a product of all diagonal elements of the matrix. At the end, we prove that the determinant of a matrix is the same as the determinant of its transpose.
LA - eng
UR - http://eudml.org/doc/266969
ER -

References

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