Editing Tensor product (section)

=== Tensor product of multilinear forms ===
Given two [[multilinear form]]s <math>f(x_1,\dots,x_k)</math> and <math>g (x_1,\dots, x_m)</math> on a vector space <math>V</math> over the field <math>K</math> their tensor product is the multilinear form:
<math display="block">(f \otimes g) (x_1,\dots,x_{k+m}) = f(x_1,\dots,x_k) g(x_{k+1},\dots,x_{k+m}).</math><ref name="An Introduction to Manifolds">{{cite book |title=An Introduction to Manifolds | first=L. W. | last=Tu |series=Universitext |publisher=Springer | page=25 | isbn=978-1-4419-7399-3 | year=2010}}</ref>

This is a special case of the [[#General tensors|product of tensors]] if they are seen as multilinear maps (see also [[Tensor#As multilinear maps|tensors as multilinear maps]]). Thus the components of the tensor product of multilinear forms can be computed by the [[Kronecker product]].