\begin{definition}[Definition:Orthogonal Matrix]
Let $R$ be a ring with unity.
Let $\mathbf Q$ be an invertible square matrix over $R$.
Then $\mathbf Q$ is '''orthogonal''' {{iff}}:
:$\mathbf Q^{-1} = \mathbf Q^\intercal$
where:
:$\mathbf Q^{-1}$ is the inverse of $\mathbf Q$
:$\mathbf Q^\intercal$ is the transpose of $\mathbf Q$
\end{definition}