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2008 | 16 | 2 | 195-202
Tytuł artykułu

Invertibility of Matrices of Field Elements

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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
Słowa kluczowe
Wydawca
Rocznik
Tom
16
Numer
2
Strony
195-202
Opis fizyczny
Daty
wydano
2008-01-01
online
2009-03-20
Twórcy
  • Shinshu University, Nagano, Japan
autor
  • Shinshu University, Nagano, Japan
autor
  • Nan Kai Institute of Technology, Nantou County, Taiwan
Bibliografia
  • [1] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
  • [2] Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990.
  • [3] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
  • [4] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
  • [5] Shigeru Furuya. Matrix and Determinant. Baifuukan (in Japanese), 1957.
  • [6] Felix R. Gantmacher. The Theory of Matrices. AMS Chelsea Publishing, 1959.
  • [7] Katarzyna Jankowska. Matrices. Abelian group of matrices. Formalized Mathematics, 2(4):475-480, 1991.
  • [8] Eugeniusz Kusak, Wojciech Leończuk, and Michał Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335-342, 1990.
  • [9] Takaya Nishiyama and Yasuho Mizuhara. Binary arithmetics. Formalized Mathematics, 4(1):83-86, 1993.
  • [10] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1(2):329-334, 1990.
  • [11] Wojciech A. Trybulec. Binary operations on finite sequences. Formalized Mathematics, 1(5):979-981, 1990.
  • [12] Wojciech A. Trybulec. Groups. Formalized Mathematics, 1(5):821-827, 1990.
  • [13] Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.
  • [14] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
  • [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] Xiaopeng Yue, Xiquan Liang, and Zhongpin Sun. Some properties of some special matrices. Formalized Mathematics, 13(4):541-547, 2005.
  • [17] Katarzyna Zawadzka. The sum and product of finite sequences of elements of a field. Formalized Mathematics, 3(2):205-211, 1992.
  • [18] Katarzyna Zawadzka. The product and the determinant of matrices with entries in a field. Formalized Mathematics, 4(1):1-8, 1993.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_v10037-008-0025-z
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