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- Cokernel abstract "In mathematics, the cokernel of a linear mapping of vector spaces f : X → Y is the quotient space Y/im(f) of the codomain of f by the image of f. The dimension of the cokernel is called the corank of f.Cokernels are dual to the kernels of category theory, hence the name: the kernel is a subobject of the domain (it maps to the domain), while the cokernel is a quotient object of the codomain (it maps from the codomain).Intuitively, given an equation f(x) = y that one is seeking to solve,the cokernel measures the constraints that y must satisfy for this equation to have a solution – the obstructions to a solution – while the kernel measures the degrees of freedom in a solution, if one exists. This is elaborated in intuition, below.More generally, the cokernel of a morphism f : X → Y in some category (e.g. a homomorphism between groups or a bounded linear operator between Hilbert spaces) is an object Q and a morphism q : Y → Q such that the composition q f is the zero morphism of the category, and furthermore q is universal with respect to this property. Often the map q is understood, and Q itself is called the cokernel of f.In many situations in abstract algebra, such as for abelian groups, vector spaces or modules, the cokernel of the homomorphism f : X → Y is the quotient of Y by the image of f. In topological settings, such as with bounded linear operators between Hilbert spaces, one typically has to take the closure of the image before passing to the quotient.".
- Cokernel thumbnail Cokernel-01.png?width=300.
- Cokernel wikiPageID "279715".
- Cokernel wikiPageLength "7139".
- Cokernel wikiPageOutDegree "59".
- Cokernel wikiPageRevisionID "671249326".
- Cokernel wikiPageWikiLink Abelian_category.
- Cokernel wikiPageWikiLink Abelian_group.
- Cokernel wikiPageWikiLink Abstract_algebra.
- Cokernel wikiPageWikiLink Bounded_linear_operator.
- Cokernel wikiPageWikiLink Bounded_operator.
- Cokernel wikiPageWikiLink Categories_for_the_Working_Mathematician.
- Cokernel wikiPageWikiLink Category:Abstract_algebra.
- Cokernel wikiPageWikiLink Category:Category_theory.
- Cokernel wikiPageWikiLink Category:Isomorphism_theorems.
- Cokernel wikiPageWikiLink Category_of_groups.
- Cokernel wikiPageWikiLink Category_theory.
- Cokernel wikiPageWikiLink Closure_(mathematics).
- Cokernel wikiPageWikiLink Codomain.
- Cokernel wikiPageWikiLink Coequalizer.
- Cokernel wikiPageWikiLink Coimage.
- Cokernel wikiPageWikiLink Commutative_diagram.
- Cokernel wikiPageWikiLink Conjugate_closure.
- Cokernel wikiPageWikiLink Dual_(category_theory).
- Cokernel wikiPageWikiLink Epimorphism.
- Cokernel wikiPageWikiLink Equivalence_class.
- Cokernel wikiPageWikiLink Exact_sequence.
- Cokernel wikiPageWikiLink Group_(mathematics).
- Cokernel wikiPageWikiLink Group_homomorphism.
- Cokernel wikiPageWikiLink Hilbert_space.
- Cokernel wikiPageWikiLink Homomorphism.
- Cokernel wikiPageWikiLink Ideal_(ring_theory).
- Cokernel wikiPageWikiLink Image_(category_theory).
- Cokernel wikiPageWikiLink Image_(mathematics).
- Cokernel wikiPageWikiLink Isomorphism.
- Cokernel wikiPageWikiLink Kernel_(algebra).
- Cokernel wikiPageWikiLink Kernel_(category_theory).
- Cokernel wikiPageWikiLink Linear_map.
- Cokernel wikiPageWikiLink Linear_mapping.
- Cokernel wikiPageWikiLink Mathematics.
- Cokernel wikiPageWikiLink Module_(mathematics).
- Cokernel wikiPageWikiLink Monomorphism.
- Cokernel wikiPageWikiLink Morphism.
- Cokernel wikiPageWikiLink Normal_closure_(group_theory).
- Cokernel wikiPageWikiLink Normal_morphism.
- Cokernel wikiPageWikiLink Preadditive_category.
- Cokernel wikiPageWikiLink Quotient_group.
- Cokernel wikiPageWikiLink Quotient_object.
- Cokernel wikiPageWikiLink Quotient_set.
- Cokernel wikiPageWikiLink Quotient_space_(linear_algebra).
- Cokernel wikiPageWikiLink Saunders_Mac_Lane.
- Cokernel wikiPageWikiLink Subgroup.
- Cokernel wikiPageWikiLink Subobject.
- Cokernel wikiPageWikiLink Topology.
- Cokernel wikiPageWikiLink Universal_mapping_property.
- Cokernel wikiPageWikiLink Universal_property.
- Cokernel wikiPageWikiLink Up_to.
- Cokernel wikiPageWikiLink Vector_space.
- Cokernel wikiPageWikiLink Vector_spaces.
- Cokernel wikiPageWikiLink Zero_morphism.
- Cokernel wikiPageWikiLink File:Cokernel-01.png.
- Cokernel wikiPageWikiLink File:Cokernel-02.png.
- Cokernel wikiPageWikiLinkText "''co''kernel".
- Cokernel wikiPageWikiLinkText "Cokernel".
- Cokernel wikiPageWikiLinkText "Left null space".
- Cokernel wikiPageWikiLinkText "coker".
- Cokernel wikiPageWikiLinkText "cokernel".
- Cokernel wikiPageWikiLinkText "ordinary cokernel from group theory".
- Cokernel hasPhotoCollection Cokernel.
- Cokernel wikiPageUsesTemplate Template:No_footnotes.
- Cokernel wikiPageUsesTemplate Template:Redirect.
- Cokernel subject Category:Abstract_algebra.
- Cokernel subject Category:Category_theory.
- Cokernel subject Category:Isomorphism_theorems.
- Cokernel hypernym Im.
- Cokernel type Article.
- Cokernel type GolfPlayer.
- Cokernel type Article.
- Cokernel type Function.
- Cokernel type Morphism.
- Cokernel type Theorem.
- Cokernel comment "In mathematics, the cokernel of a linear mapping of vector spaces f : X → Y is the quotient space Y/im(f) of the codomain of f by the image of f.".
- Cokernel label "Cokernel".
- Cokernel sameAs Conoyau.
- Cokernel sameAs Conucleo.
- Cokernel sameAs 余核.
- Cokernel sameAs 여핵.
- Cokernel sameAs Cokern.
- Cokernel sameAs m.01pn81.
- Cokernel sameAs Коядро_(теория_категорий).
- Cokernel sameAs Q2156511.
- Cokernel sameAs Q2156511.
- Cokernel wasDerivedFrom Cokernel?oldid=671249326.
- Cokernel depiction Cokernel-01.png.
- Cokernel isPrimaryTopicOf Cokernel.