Tensor product of quadratic forms
In mathematics, the tensor product of quadratic forms is most easily understood when one views the quadratic forms as quadratic spaces. If R is a commutative ring where 2 is invertible (that is, R has characteristic  ), and if  and  are two quadratic spaces over R, then their tensor product  is the quadratic space whose underlying R-module is the tensor product  of R-modules and whose quadratic form is the quadratic form associated to the tensor product of the bilinear forms associated to  and . In particular, the form  satisfies

(which does uniquely characterize it however). It follows from this that if the quadratic forms are diagonalizable (which is always possible if 2 is invertible in R), i.e., 

then the tensor product has diagonalization

Quadratic forms
Tensors