Definition:Special Orthogonal Group
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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: $\text{(iv) (c)}$