Polynomials on vector spaces

In mathematics, if F is a field, a F-valued polynomial of degree ≤ p on a vector space V is a map P : V → F of the form

$P(v)=\sum _{k=0}^{p}A_{k}(v,\dots ,v)$

for v ∈ V and A_k ∈ L^k_sym = the set of all F-valued symmetric k-linear forms for k = 0, ..., p.

References

• Ralph Abraham, Joel Robbin. Transversal Mapppings and Flows, p 7. W. A. Benjamin Inc. 1967.