Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Formalized Mathematics

(a computer assisted approach)

Editor-in-Chief: Matuszewski, Roman

4 Issues per year


SCImago Journal Rank (SJR) 2016: 0.207
Source Normalized Impact per Paper (SNIP) 2016: 0.315

Open Access
Online
ISSN
1898-9934
See all formats and pricing
More options …
Volume 14, Issue 1 (Jan 2006)

Issues

Determinant of Some Matrices of Field Elements

Yatsuka Nakamura
  • Shinshu University, Nagano, Japan, ynakamur@cs.shinshu-u.ac.jp
Published Online: 2008-06-13 | DOI: https://doi.org/10.2478/v10037-006-0001-4

Determinant of Some Matrices of Field Elements

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.

  • [1] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.Google Scholar

  • [2] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.Google Scholar

  • [3] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.Google Scholar

  • [4] Czesław Byliński. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.Google Scholar

  • [5] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.Google Scholar

  • [6] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.Google Scholar

  • [7] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.Google Scholar

  • [8] Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.Google Scholar

  • [9] Czesław Byliński. Some properties of restrictions of finite sequences. Formalized Mathematics, 5(2):241-245, 1996.Google Scholar

  • [10] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.Google Scholar

  • [11] Katarzyna Jankowska. Matrices. Abelian group of matrices. Formalized Mathematics, 2(4):475-480, 1991.Google Scholar

  • [12] Katarzyna Jankowska. Transpose matrices and groups of permutations. Formalized Mathematics, 2(5):711-717, 1991.Google Scholar

  • [13] Jarosław Kotowicz. Functions and finite sequences of real numbers. Formalized Mathematics, 3(2):275-278, 1992.Google Scholar

  • [14] Eugeniusz Kusak, Wojciech Leończuk, and Michał Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335-342, 1990.Google Scholar

  • [15] Yatsuka Nakamura and Roman Matuszewski. Reconstructions of special sequences. Formalized Mathematics, 6(2):255-263, 1997. http://fm.mizar.org/1997-6/pdf6-2/jordan3.pdf

  • [16] Takaya Nishiyama and Yasuho Mizuhara. Binary arithmetics. Formalized Mathematics, 4(1):83-86, 1993.Google Scholar

  • [17] Library Committee of the Association of Mizar Users. Binary operations on numbers. To appear in Formalized Mathematics.Google Scholar

  • [18] Andrzej Trybulec. Subsets of complex numbers. To appear in Formalized Mathematics.Google Scholar

  • [19] Andrzej Trybulec. Tarski Grothendieck set theory. Formalized Mathematics, 1(1):9-11, 1990.Google Scholar

  • [20] Andrzej Trybulec and Agata Darmochwał. Boolean domains. Formalized Mathematics, 1(1):187-190, 1990.Google Scholar

  • [21] Wojciech A. Trybulec. Binary operations on finite sequences. Formalized Mathematics, 1(5):979-981, 1990.Google Scholar

  • [22] Wojciech A. Trybulec. Groups. Formalized Mathematics, 1(5):821-827, 1990.Google Scholar

  • [23] Wojciech A. Trybulec. Pigeon hole principle. Formalized Mathematics, 1(3):575-579, 1990.Google Scholar

  • [24] Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.Google Scholar

  • [25] Wojciech A. Trybulec. Lattice of subgroups of a group. Frattini subgroup. Formalized Mathematics, 2(1):41-47, 1991.Google Scholar

  • [26] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.Google Scholar

  • [27] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.Google Scholar

  • [28] Katarzyna Zawadzka. The product and the determinant of matrices with entries in a field. Formalized Mathematics, 4(1):1-8, 1993.Google Scholar

About the article


Published Online: 2008-06-13

Published in Print: 2006-01-01


Citation Information: Formalized Mathematics, ISSN (Online) 1898-9934, ISSN (Print) 1426-2630, DOI: https://doi.org/10.2478/v10037-006-0001-4.

Export Citation

This content is open access.

Comments (0)

Please log in or register to comment.
Log in