Consider an example of an ($n\times n$) orthogonal transformation matrix $$\mathbf{S}= \left( \begin{array}{cccccccc} 1 & 0 & \dots & 0 & 0 & \dots & 0 & 0 \\ 0 & 1 & \dots & 0 & 0 & \dots & 0 & 0 \\ \dots & \dots & \dots & \dots & \dots & \dots & 0 & \dots \\ 0 & 0 & \dots & \cos\theta & 0 & \dots & 0 & \sin\theta \\ 0 & 0 & \dots & 0 & 1 & \dots & 0 & 0 \\ \dots & \dots & \dots & \dots & \dots & \dots & 1 & \dots \\ 0 & 0 & \dots & -\sin\theta & 0 & \dots & 0 & \cos\theta \end{array} \right)$$ with property $\mathbf{S^{T}} = \mathbf{S^{-1}}$. It performs a plane rotation around an angle $\theta$ in the Euclidean $n-$dimensional space.