REPOZYTORIUM UNIWERSYTETU
W BIAŁYMSTOKU
UwB

Proszę używać tego identyfikatora do cytowań lub wstaw link do tej pozycji: http://hdl.handle.net/11320/21068
Pełny rekord metadanych
Pole DCWartośćJęzyk
dc.contributor.authorPąk, Karol-
dc.date.accessioned2026-09-18T11:55:02Z-
dc.date.available2026-09-18T11:55:02Z-
dc.date.issued2008-
dc.identifier.citationFormalized Mathematics, Volume 16, Issue 3, 2008, Pages 269-275pl
dc.identifier.issn1426-2630-
dc.identifier.urihttp://hdl.handle.net/11320/21068-
dc.description.abstractThe paper is concerned with a generalization of concepts introduced in [13], i.e. introduced are matrices of linear transformations over a finite dimensional vector space. Introduced are linear transformations over a finited imensional vector space depending on a given matrix of the transformation. Finally, I prove that the rank of linear transformations over a finite-dimensional vector space is the same as the rank of the matrix of that transformation.pl
dc.language.isoenpl
dc.publisherUniversity of Białystokpl
dc.rightsAttribution-ShareAlike 4.0 Internationalpl
dc.rights.urihttps://creativecommons.org/licenses/by-sa/4.0/-
dc.titleLinear Map of Matricespl
dc.typeArticlepl
dc.rights.holder© 2009 Karol Pąk, published by University of Białystokpl
dc.rights.holderThis work is licensed under the Creative Commons License.pl
dc.identifier.doi10.2478/v10037-008-0032-0-
dc.description.AffiliationInstitute of Computer Science, University of Białystok, Polandpl
dc.description.referencesJesse Alama. The rank+nullity theorem. Formalized Mathematics, 15(3):137–142, 2007.pl
dc.description.referencesGrzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377–382, 1990.pl
dc.description.referencesGrzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41–46, 1990.pl
dc.description.referencesGrzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finitesequences. Formalized Mathematics, 1(1):107–114, 1990.pl
dc.description.referencesCzesław Byliński. Binary operations applied to finite sequences. Formalized Mathematics, 1(4):643–649, 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. Partial functions. Formalized Mathematics, 1(2):357–367, 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, 1991pl
dc.description.referencesJarosław Kotowicz. Functions and finite sequences of real numbers. Formalized Mathematics, 3(2):275–278, 1992.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.referencesRobert Milewski. Associated matrix of linear map. Formalized Mathematics, 5(3):339-345, 1996.pl
dc.description.referencesMichał Muzalewski. Rings and modules– part II. Formalized Mathematics, 2(4):579–585, 1991.pl
dc.description.referencesKarol P¸ak. Basic properties of the rank of matrices over a field. Formalized Mathematics, 15(4):199–211, 2007.pl
dc.description.referencesKarol Pąk. Block diagonal matrices. Formalized Mathematics, 16(3):259–267, 2008.pl
dc.description.referencesKarol Pąk. Solutions of linear equations. Formalized Mathematics, 16(1):81–90, 2008.pl
dc.description.referencesWojciech A. Trybulec. Basis of vector space. Formalized Mathematics, 1(5):883–885, 1990.pl
dc.description.referencesWojciech A. Trybulec. Groups. Formalized Mathematics, 1(5):821–827, 1990.pl
dc.description.referencesWojciech A. Trybulec. Linear combinations in vector space. Formalized Mathematics, 1(5):877–882, 1990.pl
dc.description.referencesWojciech A. Trybulec. Operations on subspaces in vector space. Formalized Mathematics, 1(5):871–876, 1990.pl
dc.description.referencesWojciech A. Trybulec. Subspaces and cosets of subspaces in vector space. Formalized Mathematics, 1(5):865–870, 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.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.referencesMariusz Żynel. The Steinitz theorem and the dimension of a vector space. Formalized Mathematics, 5(3):423–428, 1996.pl
dc.identifier.eissn1898-9934-
dc.description.volume16pl
dc.description.issue3pl
dc.description.firstpage269pl
dc.description.lastpage275pl
dc.identifier.citation2Formalized Mathematicspl
Występuje w kolekcji(ach):Formalized Mathematics, 2008, Volume 16, Issue 3

Pliki w tej pozycji:
Plik Opis RozmiarFormat 
Linear_Map_of_Matrices.pdf218,23 kBAdobe PDFOtwórz
Pokaż uproszczony widok rekordu Zobacz statystyki


Pozycja ta dostępna jest na podstawie licencji Licencja Creative Commons CCL Creative Commons