\begin{definition}[Definition:Proper Orthogonal Matrix]
Let $\mathbf Q$ be an orthogonal matrix.
Then $\mathbf Q$ is a '''proper orthogonal matrix''' {{iff}}:
:$\map \det {\mathbf Q} = 1$
where $\map \det {\mathbf Q}$ is the determinant of $\mathbf Q$.
\end{definition}