Let $V$ be an inner product space and $T$ be a linear transformation from $V$ to $V$.
<aside> 💡 $T$ is said to be orthogonal transformation if $\langle Tv,Tw \rangle = \langle v, w \rangle$ for all $v,w \in V$.
</aside>
When $V=\R^n$ with the usual inner product, a linear transformation $T: \R^n \to \R^n$ is orthogonal if it preserves angles and lengths.
