Definition:Special Orthogonal Group

Definition
Let $k$ be a field.

The special ($n$th) orthogonal group (on $k$), denoted $\map {\mathrm {SO} } {n, k}$, is:
 * the set of all proper orthogonal order-$n$ square matrices over $k$
 * under (conventional) matrix multiplication.

That is: $\map {\mathrm {SO} } {n, k} = \map {\mathrm O} {n, k} \cap \SL {n, k}$

Also see

 * Definition:Orthogonal Group
 * Definition:Special Unitary Group
 * Special Orthogonal Group is Group
 * Special Orthogonal Group is Subgroup of Orthogonal Group