Definition:Orthogonal Group/Bilinear Form

This page is about orthogonal group of bilinear form. For other uses, see orthogonal.

Definition

Let $V$ be a vector space over a field $\mathbb K$.

Let $B: V \times V \to \mathbb K$ be a nondegenerate bilinear form.

Its orthogonal group $\map {\mathrm O} B$ is the group of invertible linear transformations $g \in \GL V$ such that:

$\forall v, w \in V : \map B {g v, g w} = \map B {v, w}$

Also see

• Definition:Orthogonal Group

• Results about orthogonal groups of bilinear forms can be found here.

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