Linear Mapping
A linear mapping is a homomorphism between two vector spaces.
Contents
Description
Consider two vector spaces: V in Rn and W in Rm. A transformation T between these vector spaces is notated as T: V -> W. This transformation is said to have a domain of Rn and a codomain of Rm.
A transformation between these two vector spaces that also preserves the structure of vector spaces is a homomorphism.
A homomorphism that is also invertible is an isomorphism.
Relation to Bases
If V and W are finite and bases are defined for both, then all homomorphisms can be expressed with matrix multiplication.