Coker

Coker may refer to:

People

Places

Municipalities

Other locations

Other uses

See also

Coker (surname)

Coker is a surname shared by several notable people, including:

List of people with the surname

Cokernel

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.