Polynomial mapping

In algebra, a polynomial mapping $P:V\to W$ 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

$P(v)=\sum _{i}L_{i}(v)^{n_{i}}w_{i}$

where $w_{i}$'a are vectors in W and $L_{i}:V\to k$ are linear functionals.