The tensor product 
of two modules over a commutative
ring 
is a module equipped with a bilinear
function 
that has the universal property among bilinear
functions out of 
.
In other words, for every 
-module 
, each 
-bilinear function 
factors uniquely
through a module homomorphism 
.
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.
For linear transformations between finite-dimensional vector spaces, the tensor product is represented by the Kronecker product of their matrices after vector bases are chosen.
