>>13296381A multilinear map from a vector space (or more generally, a module) and its dual to the scalar field.
In practice it can be treated as a multilinear map from a vector space and its dual to fewer copies of the vector space and/or dual.
A few examples of tensors are:
Vectors , dual vectors, operators on finite dimensional vector spaces and the metric tensor.
A euclidean vector is a linear map (a subset of multilinear maps) from the dual vectors to the reals, a dual vector to a euclidean vector is a linear map from the set of euclidean vectors to the reals.
A linear operator is usually thought of as a map from a vectorspace to itself, but it can also be thought of as a multilinear map wich takes in one vector and one dual vector and spits out a number. The metric tensor on the other hand takes in two vectos and spits out a number.
