Definition
38
[11H] We also define the rules
\[ \| A\| _{F-\tilde p}= \begin{cases} \sqrt[\tilde p]{∑_{i,j} |A_{i,j}|^{\tilde p}} & \tilde p {\lt}∞~ ~ ~ ,\\ \max _{i,j} |A_{i,j}| & \tilde p =∞ \end{cases} \]
for \(\tilde p∈[1,∞]\). The case \(\tilde p=2\) is called Frobenious’ norm.