Definition:Symmetric Bilinear Form

Definition
Let $R$ be a ring

Let $M$ be an $R$-module.

Let $b : M\times M \to R$ be a bilinear form.

Then $b$ is symmetric $b(v,w) = b(w,v)$ for all $v,w\in M$.

Also see

 * Definition:Quadratic Form
 * Definition:Alternating Bilinear Form
 * Definition:Reflexive Bilinear Form