Definition:Symmetric Bilinear Form/Nondegenerate

Definition
Let $\Bbb K$ be a field.

Let $V$ be a vector space over $\Bbb K$.

Let $b: V \times V \to \Bbb K$ be a symmetric bilinear form.

Let $b$ be a nondegenerate bilinear form.

Then $b$ is a nondegenerate symmetric bilinear form.

Also known as
Some texts refer to $b$ as a '''scalar product.