Category:Orthogonal Groups

This category contains results about Orthogonal Groups.

Let $k$ be a field.

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

$\map {\mathrm O} {n, k} := \set {M \in \GL {n, k}: M^\intercal = M^{-1} }$

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