Definition:Symmetric Bilinear Form/Nondegenerate
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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.
Sources
- Weisstein, Eric W. "Symmetric Bilinear Form." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SymmetricBilinearForm.html