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  3. Formalized Mathematics
  4. Formalized Mathematics, 2007, Volume 15, Issue 3

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    • Proszę używać tego identyfikatora do cytowań lub wstaw link do tej pozycji: http://hdl.handle.net/11320/21389
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    Pole DCWartośćJęzyk
    dc.contributor.authorPąk, Karol-
    dc.contributor.authorTrybulec, Andrzej-
    dc.date.accessioned2026-10-30T11:08:08Z-
    dc.date.available2026-10-30T11:08:08Z-
    dc.date.issued2007-
    dc.identifier.citationFormalized Mathematics, Volume 15, Issue 3, Pages 143-150pl
    dc.identifier.issn1426-2630-
    dc.identifier.urihttp://hdl.handle.net/11320/21389-
    dc.description.abstractIn the article the formula for Laplace expansion is proved.pl
    dc.language.isoenpl
    dc.publisherUniversity of Białystokpl
    dc.rightsAttribution-ShareAlike 4.0 International (CC BY-SA 4.0)-
    dc.rights.urihttps://creativecommons.org/licenses/by-sa/4.0/-
    dc.titleLaplace Expansionpl
    dc.typeArticlepl
    dc.rights.holder© 2008 Karol Pak, Andrzej Trybulec, published by University of Białystokpl
    dc.rights.holderThis work is licensed under the Creative Commons License.pl
    dc.identifier.doi10.2478/v10037-007-0016-5-
    dc.description.AffiliationKarol Pąk - Institute of Computer Science, University of Białystok, Polandpl
    dc.description.AffiliationAndrzej Trybulec - Institute of Computer Science, University of Białystok, Polandpl
    dc.description.referencesGrzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.pl
    dc.description.referencesGrzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.pl
    dc.description.referencesGrzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.pl
    dc.description.referencesCzesław Byliński. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.pl
    dc.description.referencesCzesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990.pl
    dc.description.referencesCzesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.pl
    dc.description.referencesCzesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.pl
    dc.description.referencesCzesław 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.pl
    dc.description.referencesCzesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.pl
    dc.description.referencesCzesław Byliński. Semigroup operations on finite subsets. Formalized Mathematics, 1(4):651-656, 1990.pl
    dc.description.referencesCzesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.pl
    dc.description.referencesAgata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.pl
    dc.description.referencesKatarzyna Jankowska. Matrices. Abelian group of matrices. Formalized Mathematics, 2(4):475-480, 1991.pl
    dc.description.referencesKatarzyna Jankowska. Transpose matrices and groups of permutations. Formalized Mathematics, 2(5):711-717, 1991.pl
    dc.description.referencesEugeniusz Kusak, Wojciech Leończuk, and Michał Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335-342, 1990.pl
    dc.description.referencesRafał Kwiatek. Factorial and Newton coefficients. Formalized Mathematics, 1(5):887-890, 1990.pl
    dc.description.referencesYatsuka Nakamura. Determinant of some matrices of field elements. Formalized Mathematics, 14(1):1-5, 2006.pl
    dc.description.referencesTakaya Nishiyama and Yasuho Mizuhara. Binary arithmetics. Formalized Mathematics, 4(1):83-86, 1993.pl
    dc.description.referencesAndrzej Trybulec. Semilattice operations on finite subsets. Formalized Mathematics, 1(2):369-376, 1990.pl
    dc.description.referencesAndrzej Trybulec. Tarski Grothendieck set theory. Formalized Mathematics, 1(1):9-11, 1990.pl
    dc.description.referencesAndrzej Trybulec and Agata Darmochwał. Boolean domains. Formalized Mathematics, 1(1):187-190, 1990.pl
    dc.description.referencesWojciech A. Trybulec. Binary operations on finite sequences. Formalized Mathematics, 1(5):979-981, 1990.pl
    dc.description.referencesWojciech A. Trybulec. Groups. Formalized Mathematics, 1(5):821-827, 1990.pl
    dc.description.referencesWojciech A. Trybulec. Non-contiguous substrings and one-to-one finite sequences. Formalized Mathematics, 1(3):569-573, 1990.pl
    dc.description.referencesWojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.pl
    dc.description.referencesZinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.pl
    dc.description.referencesEdmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.pl
    dc.description.referencesEdmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.pl
    dc.description.referencesXiaopeng Yue, Xiquan Liang, and Zhongpin Sun. Some properties of some special matrices. Formalized Mathematics, 13(4):541-547, 2005.pl
    dc.description.referencesKatarzyna Zawadzka. The sum and product of finite sequences of elements of a field. Formalized Mathematics, 3(2):205-211, 1992.pl
    dc.description.referencesKatarzyna Zawadzka. The product and the determinant of matrices with entries in a field. Formalized Mathematics, 4(1):1-8, 1993.pl
    dc.description.referencesKarol Pąk. Basic properties of determinants of square matrices over a field. Formalized Mathematics, 15(1):17-25, 2007.1pl
    dc.description.referencesAndrzej Trybulec. Subsets of complex numbers. To appear in Formalized Mathematics.pl
    dc.description.referencesAndrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1(2):329-334, 1990.pl
    dc.description.volume15pl
    dc.description.issue3pl
    dc.description.firstpage143pl
    dc.description.lastpage150pl
    dc.identifier.citation2Formalized Mathematicspl
    Występuje w kolekcji(ach):Artykuły naukowe (WInf)
    Formalized Mathematics, 2007, Volume 15, Issue 3

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