Definition:Symmetric Bilinear Form/Nondegenerate

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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.