About: 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 then the tensor product has diagonalization * v * t * e