Polynomial mapping
In algebra, a polynomial map or polynomial mapping between vector spaces over an infinite field k is a polynomial in linear functionals with coefficients in W; i.e., it can be written as
where the are linear functionals and the are vectors in W. For example, if, then a polynomial mapping can be expressed as where the are polynomial functions on V.
When V, W are finite-dimensional vector spaces and are viewed as algebraic varieties, then a polynomial mapping is precisely a morphism of algebraic varieties.
One fundamental outstanding question regarding polynomial mappings is the Jacobian conjecture, which concerns the sufficiency of a polynomial mapping to be invertible.
