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

Sources

• 1964: Walter Ledermann: Introduction to the Theory of Finite Groups (5th ed.) ... (previous) ... (next): Chapter $\text {I}$: The Group Concept: $\S 3$: Examples of Infinite Groups: $\text{(iv) (c)}$