Multilineal Map

Given the vectorial Space V, F an aplicattion such us

     F: Vx...(n veces)...xV → R

It is said that F is multilinear if

    1) F(x1, x2, ...,λxk,..., xn) = λF(x1, x2, ...,xk,..., xn), ∀λ∈R, ∀x1, ..., xn ∈V, 1≤k≤n

    2) F(x1, x2, ...xk + y,..., xn) = F(x1, x2, ...,xk,..., xn) + F(x1, x2, ...,y,..., xn), ∀λ∈R, ∀x1, ..., xn, y ∈V, 1≤k≤n