The tensor product 
of two modules over a commutative
ring 
is a module equipped with a bilinear function 
that is universal
among bilinear functions out of 
. In other words, every bilinear
function 
factors uniquely through a linear function 
.
The construction specializes to the vector space tensor product when 
is a field. Tensor products also
occur for group representations, sheaves
of modules, vector bundles, and other algebraic
objects.
After bases are chosen, the tensor product of two linear transformations is represented by the Kronecker product of their matrices.
