# 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 if and only if:

$\forall v, w, \in M: b \left({v, w}\right) = b \left({w, v}\right)$