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Formalized Mathematics

(a computer assisted approach)

Editor-in-Chief: Matuszewski, Roman

4 Issues per year


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ISSN
1898-9934
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Volume 15, Issue 3 (Jan 2007)

Issues

Laplace Expansion

Karol Pak
  • Institute of Computer Science, University of Białystok, Poland
/ Andrzej Trybulec
  • Institute of Computer Science, University of Białystok, Poland
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.

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  • [2] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.

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

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

  • [5] Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990.

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

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

  • [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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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