Proszę używać tego identyfikatora do cytowań lub wstaw link do tej pozycji:
http://hdl.handle.net/11320/21068Pełny rekord metadanych
| Pole DC | Wartość | Język |
|---|---|---|
| dc.contributor.author | Pąk, Karol | - |
| dc.date.accessioned | 2026-09-18T11:55:02Z | - |
| dc.date.available | 2026-09-18T11:55:02Z | - |
| dc.date.issued | 2008 | - |
| dc.identifier.citation | Formalized Mathematics, Volume 16, Issue 3, 2008, Pages 269-275 | pl |
| dc.identifier.issn | 1426-2630 | - |
| dc.identifier.uri | http://hdl.handle.net/11320/21068 | - |
| dc.description.abstract | The 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.iso | en | pl |
| dc.publisher | University of Białystok | pl |
| dc.rights | Attribution-ShareAlike 4.0 International | pl |
| dc.rights.uri | https://creativecommons.org/licenses/by-sa/4.0/ | - |
| dc.title | Linear Map of Matrices | pl |
| dc.type | Article | pl |
| dc.rights.holder | © 2009 Karol Pąk, published by University of Białystok | pl |
| dc.rights.holder | This work is licensed under the Creative Commons License. | pl |
| dc.identifier.doi | 10.2478/v10037-008-0032-0 | - |
| dc.description.Affiliation | Institute of Computer Science, University of Białystok, Poland | pl |
| dc.description.references | Jesse Alama. The rank+nullity theorem. Formalized Mathematics, 15(3):137–142, 2007. | pl |
| dc.description.references | Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377–382, 1990. | pl |
| dc.description.references | Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41–46, 1990. | pl |
| dc.description.references | Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finitesequences. Formalized Mathematics, 1(1):107–114, 1990. | pl |
| dc.description.references | Czesław Byliński. Binary operations applied to finite sequences. Formalized Mathematics, 1(4):643–649, 1990. | pl |
| dc.description.references | Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990. | pl |
| dc.description.references | Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153–164, 1990. | pl |
| dc.description.references | Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357–367, 1990. | pl |
| dc.description.references | Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165–167, 1990. | pl |
| dc.description.references | Katarzyna Jankowska. Matrices. Abelian group of matrices. Formalized Mathematics, 2(4):475–480, 1991 | pl |
| dc.description.references | Jarosław Kotowicz. Functions and finite sequences of real numbers. Formalized Mathematics, 3(2):275–278, 1992. | pl |
| dc.description.references | Eugeniusz Kusak, Wojciech Leończuk, and Michał Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335–342, 1990. | pl |
| dc.description.references | Robert Milewski. Associated matrix of linear map. Formalized Mathematics, 5(3):339-345, 1996. | pl |
| dc.description.references | Michał Muzalewski. Rings and modules– part II. Formalized Mathematics, 2(4):579–585, 1991. | pl |
| dc.description.references | Karol P¸ak. Basic properties of the rank of matrices over a field. Formalized Mathematics, 15(4):199–211, 2007. | pl |
| dc.description.references | Karol Pąk. Block diagonal matrices. Formalized Mathematics, 16(3):259–267, 2008. | pl |
| dc.description.references | Karol Pąk. Solutions of linear equations. Formalized Mathematics, 16(1):81–90, 2008. | pl |
| dc.description.references | Wojciech A. Trybulec. Basis of vector space. Formalized Mathematics, 1(5):883–885, 1990. | pl |
| dc.description.references | Wojciech A. Trybulec. Groups. Formalized Mathematics, 1(5):821–827, 1990. | pl |
| dc.description.references | Wojciech A. Trybulec. Linear combinations in vector space. Formalized Mathematics, 1(5):877–882, 1990. | pl |
| dc.description.references | Wojciech A. Trybulec. Operations on subspaces in vector space. Formalized Mathematics, 1(5):871–876, 1990. | pl |
| dc.description.references | Wojciech A. Trybulec. Subspaces and cosets of subspaces in vector space. Formalized Mathematics, 1(5):865–870, 1990. | pl |
| dc.description.references | Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291–296, 1990. | pl |
| dc.description.references | Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67–71, 1990. | pl |
| dc.description.references | Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73–83, 1990. | pl |
| dc.description.references | Xiaopeng Yue, Xiquan Liang, and Zhongpin Sun. Some properties of some special matrices. Formalized Mathematics, 13(4):541–547, 2005. | pl |
| dc.description.references | Katarzyna Zawadzka. The sum and product of finite sequences of elements of a field. Formalized Mathematics, 3(2):205–211, 1992. | pl |
| dc.description.references | Katarzyna Zawadzka. The product and the determinant of matrices with entries in a field. Formalized Mathematics, 4(1):1–8, 1993. | pl |
| dc.description.references | Mariusz Żynel. The Steinitz theorem and the dimension of a vector space. Formalized Mathematics, 5(3):423–428, 1996. | pl |
| dc.identifier.eissn | 1898-9934 | - |
| dc.description.volume | 16 | pl |
| dc.description.issue | 3 | pl |
| dc.description.firstpage | 269 | pl |
| dc.description.lastpage | 275 | pl |
| dc.identifier.citation2 | Formalized Mathematics | pl |
| Występuje w kolekcji(ach): | Formalized Mathematics, 2008, Volume 16, Issue 3 | |
Pliki w tej pozycji:
| Plik | Opis | Rozmiar | Format | |
|---|---|---|---|---|
| Linear_Map_of_Matrices.pdf | 218,23 kB | Adobe PDF | Otwórz |
Pozycja ta dostępna jest na podstawie licencji Licencja Creative Commons CCL
