Solution
= Solution
A real square <orthogonal matrix> $Q$ satisfies $\boxed{Q^TQ=QQ^T=I}$. Equivalently its columns form an <orthonormal basis>. In particular it preserves the <Euclidean norm>, since $\|Qx\|_2^2=x^TQ^TQx=\|x\|_2^2$.
= Solution
A real square <orthogonal matrix> $Q$ satisfies $\boxed{Q^TQ=QQ^T=I}$. Equivalently its columns form an <orthonormal basis>. In particular it preserves the <Euclidean norm>, since $\|Qx\|_2^2=x^TQ^TQx=\|x\|_2^2$.