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, 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
. It follows from this that if the quadratic forms are diagonalizable, i.e.,
then the tensor product has diagonalization
