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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  1. [1] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990. 
  2. [2] Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990. 
  3. [3] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990. 
  4. [4] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990. 
  5. [5] Shigeru Furuya. Matrix and Determinant. Baifuukan (in Japanese), 1957. 
  6. [6] Felix R. Gantmacher. The Theory of Matrices. AMS Chelsea Publishing, 1959. Zbl0022.31503
  7. [7] Katarzyna Jankowska. Matrices. Abelian group of matrices. Formalized Mathematics, 2(4):475-480, 1991. 
  8. [8] Eugeniusz Kusak, Wojciech Leończuk, and Michał Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335-342, 1990. 
  9. [9] Takaya Nishiyama and Yasuho Mizuhara. Binary arithmetics. Formalized Mathematics, 4(1):83-86, 1993. 
  10. [10] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1(2):329-334, 1990. 
  11. [11] Wojciech A. Trybulec. Binary operations on finite sequences. Formalized Mathematics, 1(5):979-981, 1990. 
  12. [12] Wojciech A. Trybulec. Groups. Formalized Mathematics, 1(5):821-827, 1990. 
  13. [13] Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990. 
  14. [14] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990. 
  15. [15] Hiroshi Yamazaki, Yoshinori Fujisawa, and Yatsuka Nakamura. On replace function and swap function for finite sequences. Formalized Mathematics, 9(3):471-474, 2001. 
  16. [16] Xiaopeng Yue, Xiquan Liang, and Zhongpin Sun. Some properties of some special matrices. Formalized Mathematics, 13(4):541-547, 2005. 
  17. [17] Katarzyna Zawadzka. The sum and product of finite sequences of elements of a field. Formalized Mathematics, 3(2):205-211, 1992. 
  18. [18] Katarzyna Zawadzka. The product and the determinant of matrices with entries in a field. Formalized Mathematics, 4(1):1-8, 1993. 

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