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 15, Issue 3 (Jan 2007)

Issues

Laplace Expansion

Karol Pak / Andrzej Trybulec
Published Online: 2008-06-09 | DOI: https://doi.org/10.2478/v10037-007-0016-5

Laplace Expansion

In the article the formula for Laplace expansion is proved.

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

  • [2] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 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. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990.Google Scholar

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

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

  • [8] Czesław Byliński. The modification of a function by a function and the iteration of the composition of a function. Formalized Mathematics, 1(3):521-527, 1990.Google Scholar

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

  • [10] Czesław Byliński. Semigroup operations on finite subsets. Formalized Mathematics, 1(4):651-656, 1990.Google Scholar

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

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

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

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

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

  • [16] Rafał Kwiatek. Factorial and Newton coefficients. Formalized Mathematics, 1(5):887-890, 1990.Google Scholar

  • [17] Yatsuka Nakamura. Determinant of some matrices of field elements. Formalized Mathematics, 14(1):1-5, 2006.Google Scholar

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

  • [22] Andrzej Trybulec. Semilattice operations on finite subsets. Formalized Mathematics, 1(2):369-376, 1990.Google Scholar

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

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

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

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

  • [27] Wojciech A. Trybulec. Non-contiguous substrings and one-to-one finite sequences. Formalized Mathematics, 1(3):569-573, 1990.Google Scholar

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

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

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

  • [31] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.Google Scholar

  • [32] Xiaopeng Yue, Xiquan Liang, and Zhongpin Sun. Some properties of some special matrices. Formalized Mathematics, 13(4):541-547, 2005.Google Scholar

  • [33] Katarzyna Zawadzka. The sum and product of finite sequences of elements of a field. Formalized Mathematics, 3(2):205-211, 1992.Google Scholar

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

  • [19] Karol Pak. Basic properties of determinants of square matrices over a field. Formalized Mathematics, 15(1):17-25, 2007.Google Scholar

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

  • [21] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1(2):329-334, 1990.Google Scholar

About the article


Published Online: 2008-06-09

Published in Print: 2007-01-01


Citation Information: Formalized Mathematics, ISSN (Online) 1898-9934, ISSN (Print) 1426-2630, DOI: https://doi.org/10.2478/v10037-007-0016-5.

Export Citation

This content is open access.

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
Karol Pąk
Formalized Mathematics, 2007, Volume 15, Number 4

Comments (0)

Please log in or register to comment.
Log in