Solution
= Solution
A real square <orthogonal matrix> $Q$ satisfies
$$
\boxed{Q^TQ=I},
$$
equivalently $Q^{-1}=Q^T$. Its columns, and also its rows, form an <orthonormal basis>. Consequently it preserves <dot products> and <Euclidean norms>.
= Solution
A real square <orthogonal matrix> $Q$ satisfies
$$
\boxed{Q^TQ=I},
$$
equivalently $Q^{-1}=Q^T$. Its columns, and also its rows, form an <orthonormal basis>. Consequently it preserves <dot products> and <Euclidean norms>.