Polynomials on vector spaces

In mathematics, a polynomial of degree ≤ p on a vector space V is a map P : V → R 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 symmetric k-linear forms for k = 0, ..., p.

References

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