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  3. Formalized Mathematics
  4. Formalized Mathematics, 2006, Volume 14, Issue 3

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    • Proszę używać tego identyfikatora do cytowań lub wstaw link do tej pozycji: http://hdl.handle.net/11320/21382
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    Pole DCWartośćJęzyk
    dc.contributor.authorZhang, Bo-
    dc.contributor.authorNakamura, Yatsuka-
    dc.date.accessioned2026-10-30T09:27:58Z-
    dc.date.available2026-10-30T09:27:58Z-
    dc.date.issued2006-
    dc.identifier.citationFormalized Mathematics, Volume 14, Issue 3, Pages 101-108pl
    dc.identifier.issn1426-2630-
    dc.identifier.urihttp://hdl.handle.net/11320/21382-
    dc.description.abstractIn this article, we first define finite sequences of probability distribution and matrices of joint probability and conditional probability. We discuss also the concept of marginal probability. Further, we describe some theorems of matrices of real elements including quadratic form.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.titleThe Definition of Finite Sequences and Matrices of Probability, and Addition of Matrices of Real Elementspl
    dc.typeArticlepl
    dc.rights.holder© 2008 Bo Zhang, Yatsuka Nakamura, published by University of Białystokpl
    dc.rights.holderThis work is licensed under the Creative Commons License.pl
    dc.identifier.doi10.2478/v10037-006-0012-1-
    dc.description.AffiliationBo Zhang - Shinshu University, Nagano, Japanpl
    dc.description.AffiliationYatsuka Nakamura - Shinshu University, Nagano, Japanpl
    dc.description.referencesKanchun and Yatsuka Nakamura. The inner product of fi nite sequences and of points of n-dimensional topological space. Formalized Mathematics, 11(2):179-183, 2003.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. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.pl
    dc.description.referencesCzesław Byliński. The sum and product of finite sequences of real numbers. Formalized Mathematics, 1(4):661-668, 1990.pl
    dc.description.referencesAgata Darmochwał. The Euclidean space. Formalized Mathematics, 2(4):599-603, 1991.pl
    dc.description.referencesKatarzyna Jankowska. Matrices. Abelian group of matrices. Formalized Mathematics, 2(4):475-480, 1991.pl
    dc.description.referencesJarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990.pl
    dc.description.referencesJarosław Kotowicz and Yatsuka Nakamura. Introduction to Go-board - part I. Formalized Mathematics, 3(1):107-115, 1992.pl
    dc.description.referencesEugeniusz Kusak, Wojciech Leończuk, and Michał Muzalewski. Abelian groups, fi elds 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.referencesRobert Milewski. Associated matrix of linear map. Formalized Mathematics, 5(3):339-345, 1996.pl
    dc.description.referencesYatsuka Nakamura, Nobuyuki Tamura, and Wenpai Chang. A theory of matrices of real elements. Formalized Mathematics, 14(1):21-28, 2006.pl
    dc.description.referencesLibrary Committee of the Association of Mizar Users. Binary operations on numbers. To appear in Formalized Mathematics.pl
    dc.description.referencesAndrzej Trybulec. Subsets of complex numbers. To appear in Formalized Mathematics.pl
    dc.description.referencesAndrzej Trybulec. Tarski Grothendieck set theory. Formalized Mathematics, 1(1):9-11, 1990.pl
    dc.description.referencesWojciech A. Trybulec. Groups. Formalized Mathematics, 1(5):821-827, 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.referencesKatarzyna Zawadzka. The sum and product of fi nite sequences of elements of a fi eld. Formalized Mathematics, 3(2):205-211, 1992.pl
    dc.identifier.eissn1898-9934-
    dc.description.volume14pl
    dc.description.issue3pl
    dc.description.firstpage101pl
    dc.description.lastpage108pl
    dc.identifier.citation2Formalized Mathematicspl
    Występuje w kolekcji(ach):Formalized Mathematics, 2006, Volume 14, Issue 3

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