Polynomials on vector spaces
for v ∈ V and Ak ∈ Lksym = the set of all F-valued symmetric k-linear forms for k = 0, ..., p. P is called homogeneous of degree p if P = Ap above.
Similarly, one can define an n-variable F-valued polynomial of degree ≤ p on V to be
where Ai,j,k ∈ Lpi,j,ksym with . In this case P is called homogeneous if we only have the k = p summand in the above expression.
- Ralph Abraham, Joel Robbin. Transversal Mapppings and Flows, p 7. W. A. Benjamin Inc. 1967.
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