# Category:Orthogonal Groups

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This category contains results about Orthogonal Groups.

Let $k$ be a field.

The ($n$th) orthogonal group (on $k$), denoted $\operatorname O \left({n, k}\right)$, is the following subset of the general linear group $\operatorname{GL} \left({n, k}\right)$:

$\operatorname O \left({n, k}\right) := \left\{ {M \in \operatorname{GL} \left({n, k}\right): M^\intercal = M^{-1} }\right\}$

where $M^\intercal$ denotes the transpose of $M$.

## Pages in category "Orthogonal Groups"

The following 5 pages are in this category, out of 5 total.