Is there a name for a vector space together with a bilinear form?

Question

I know about inner product spaces, but I need to consider a more general setting:

An $F$-vector space $V$ together with a bilinear function $V\times V\to F$.

Is there some name for this that is commonly used?

Answer 1

The closest thing I've seen is "semi-indefinite-inner product space" (https://arxiv.org/abs/0901.4872) which does not require the bilinear function to be symmetric or positive, but does impose a non-degeneracy condition and the Cauchy-Schwarz inequality.

As Will points out there is also "quadratic space," if your bilinear function is symmetric.