Definition:Orthogonal Group/Inner Product Space

This page is about orthogonal group of inner product space. For other uses, see orthogonal.

Definition

Let $V$ be an inner product space.

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

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

That is, it is the orthogonal group of its inner product.

Also see

• Results about orthogonal groups of inner product spaces can be found here.

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