Tensors
Multilinear functions. In the first chapter we studied linear and bilinear functions on an n-dimensional vector space. A natural generalization of these concepts is the concept of a multilinear function of an arbitrary number of vectors some of which are elements of V nad some of which are elements of the dual space V*.
Definition 8.2.1. A function
T (x, y, ..., f, g, ...)
is said to be a multilinear function of h vectors x, y ∈ V and k covectors f, g ∈ V* (the dual of V*). If T is linear in each of its arguments.