Solution
= Solution
The relevant norm is the <operator norm> induced by the complex <Euclidean norm>, also called the <matrix 2-norm>:
$$
\boxed{\|B\|_2=\max_{q\ne0}\frac{\|Bq\|_2}{\|q\|_2}=\max_{\|q\|_2=1}\|Bq\|_2.}
$$
The maximum exists because the unit sphere in finite dimensions is compact. It obeys $\|Bq\|_2\le\|B\|_2\|q\|_2$ and is the norm relevant to the specified perturbation energy. Other matrix norms do not in general give this gain.