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| Pole DC | Wartość | Język |
|---|---|---|
| dc.contributor.author | Alama, Jesse | - |
| dc.date.accessioned | 2026-10-30T09:59:28Z | - |
| dc.date.available | 2026-10-30T09:59:28Z | - |
| dc.date.issued | 2007 | - |
| dc.identifier.citation | Formalized Mathematics, Volume 15, Issue 3, Pages 137-142 | pl |
| dc.identifier.issn | 1426-2630 | - |
| dc.identifier.uri | http://hdl.handle.net/11320/21385 | - |
| dc.description.abstract | The rank+nullity theorem states that, if T is a linear transformation from a finite-dimensional vector space V to a finite-dimensional vector space W, then dim(V) = rank(T) + nullity(T), where rank(T) = dim(im(T)) and nullity(T) = dim(ker(T)). The proof treated here is standard; see, for example, [14]: take a basis A of ker(T) and extend it to a basis B of V, and then show that dim(im(T)) is equal to |B - A|, and that T is one-to-one on B - A. | pl |
| dc.language.iso | en | pl |
| dc.publisher | University of Białystok | pl |
| dc.rights | Attribution-ShareAlike 4.0 International (CC BY-SA 4.0) | - |
| dc.rights.uri | https://creativecommons.org/licenses/by-sa/4.0/ | - |
| dc.title | The Rank+Nullity Theorem | pl |
| dc.type | Article | pl |
| dc.rights.holder | © 2008 Jesse Alama, published by University of Białystok | pl |
| dc.rights.holder | This work is licensed under the Creative Commons License. | pl |
| dc.identifier.doi | 10.2478/v10037-007-0015-6 | - |
| dc.description.Affiliation | Department of Philosophy, Stanford University, USA | pl |
| dc.description.references | Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990. | pl |
| dc.description.references | Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990. | pl |
| dc.description.references | Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990. | pl |
| dc.description.references | Grzegorz Bancerek and Andrzej Trybulec. Miscellaneous facts about functions. Formalized Mathematics, 5(4):485-492, 1996. | 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. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 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. 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.references | Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990. | pl |
| dc.description.references | Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990. | pl |
| dc.description.references | Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990. | 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 | Serge Lang. Algebra. Springer, 3rd edition, 2005. | 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 | Andrzej Trybulec. Subsets of complex numbers. To appear in Formalized Mathematics. | pl |
| dc.description.references | Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1(2):329-334, 1990. | pl |
| dc.description.references | Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics, 1(1):115-122, 1990. | pl |
| dc.description.references | Andrzej Trybulec. Function domains and Fránkel operator. Formalized Mathematics, 1(3):495-500, 1990. | pl |
| dc.description.references | Andrzej Trybulec. Tarski Grothendieck set theory. Formalized Mathematics, 1(1):9-11, 1990. | pl |
| dc.description.references | Andrzej Trybulec. Tuples, projections and Cartesian products. Formalized Mathematics, 1(1):97-105, 1990. | 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 real linear space. Formalized Mathematics, 1(3):581-588, 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. Non-contiguous substrings and one-to-one finite sequences. Formalized Mathematics, 1(3):569-573, 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. Pigeon hole principle. Formalized Mathematics, 1(3):575-579, 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 | Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990. | 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.description.volume | 15 | pl |
| dc.description.issue | 3 | pl |
| dc.description.firstpage | 137 | pl |
| dc.description.lastpage | 142 | pl |
| dc.identifier.citation2 | Formalized Mathematics | pl |
| Występuje w kolekcji(ach): | Formalized Mathematics, 2007, Volume 15, Issue 3 | |
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