Let \(V_1,\ldots,V_k\) and \(W\) be vector spaces . A map which is linear in every argument (assuming the other arguments are fixed) is called multi linear. We denote the space of all multi linear maps from \(V_1\times \cdots \times V_k\) to \(W\) with \(L(V_1,\ldots,V_k;W)\).
Remarks
- \(L(V_1,\ldots,V_k;W)\) is a vector space