Definition:Special Orthogonal Group

From ProofWiki
Jump to navigation Jump to search

Definition

Let $k$ be a field.


The special ($n$th) orthogonal group (on $k$), denoted $\operatorname {SO} \left({n, k}\right)$, is:

the set of all proper orthogonal order-$n$ square matrices over $k$
under (conventional) matrix multiplication.

That is: $\operatorname{SO}_n(k) = \operatorname{O}_n(k) \cap \operatorname{SL}_n(k)$


Also see


Sources