Invertibility of Matrices of Field Elements

Yatsuka Nakamura; Kunio Oniumi; Wenpai Chang

Formalized Mathematics (2008)

  • Volume: 16, Issue: 2, page 195-202
  • ISSN: 1426-2630

Abstract

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In this paper the theory of invertibility of matrices of field elements (see e.g. [5], [6]) is developed. The main purpose of this article is to prove that the left invertibility and the right invertibility are equivalent for a matrix of field elements. To prove this, we introduced a special transformation of matrix to some canonical forms. Other concepts as zero vector and base vectors of field elements are also introduced as a preparation.MML identifier: MATRIX14, version: 7.9.01 4.101.1015

How to cite

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Yatsuka Nakamura, Kunio Oniumi, and Wenpai Chang. "Invertibility of Matrices of Field Elements." Formalized Mathematics 16.2 (2008): 195-202. <http://eudml.org/doc/267371>.

@article{YatsukaNakamura2008,
abstract = {In this paper the theory of invertibility of matrices of field elements (see e.g. [5], [6]) is developed. The main purpose of this article is to prove that the left invertibility and the right invertibility are equivalent for a matrix of field elements. To prove this, we introduced a special transformation of matrix to some canonical forms. Other concepts as zero vector and base vectors of field elements are also introduced as a preparation.MML identifier: MATRIX14, version: 7.9.01 4.101.1015},
author = {Yatsuka Nakamura, Kunio Oniumi, Wenpai Chang},
journal = {Formalized Mathematics},
language = {eng},
number = {2},
pages = {195-202},
title = {Invertibility of Matrices of Field Elements},
url = {http://eudml.org/doc/267371},
volume = {16},
year = {2008},
}

TY - JOUR
AU - Yatsuka Nakamura
AU - Kunio Oniumi
AU - Wenpai Chang
TI - Invertibility of Matrices of Field Elements
JO - Formalized Mathematics
PY - 2008
VL - 16
IS - 2
SP - 195
EP - 202
AB - In this paper the theory of invertibility of matrices of field elements (see e.g. [5], [6]) is developed. The main purpose of this article is to prove that the left invertibility and the right invertibility are equivalent for a matrix of field elements. To prove this, we introduced a special transformation of matrix to some canonical forms. Other concepts as zero vector and base vectors of field elements are also introduced as a preparation.MML identifier: MATRIX14, version: 7.9.01 4.101.1015
LA - eng
UR - http://eudml.org/doc/267371
ER -

References

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