Orthogonal matrix norm
If $H$ is an orthogonal matrix, then $||H||=1$ and $||HA||=||A||, \forall A$-matrix (such that we can writ $H \cdot A$).
What norm is this about?
The operator norm $$ \|A\|=\max\{\|Ax\|_2:\ \|x\|=1\}, $$ where $\|\cdot\|_2$ is the Euclidean norm, also satisfies those two equalities. They follow easily from the fact that $\|y\|_2^2=y^Ty$, so $$\|Hx\|_2^2=(Hx)^THx=x^TH^THx=x^Tx=\|x\|_2^2.$$
This holds for any norm induced by an inner product. This follows from $$\|QA\|=\sqrt{(QA,QA)}=\sqrt{(Q^TQA,A)}=\sqrt{(A,A)} = \|A\|$$
With $Q$ an orthonormal matrix, i.e., $Q^{-1}=Q^T$.