The norm $\lVert A \rVert$ is different from the norm $\lVert A(x)\rVert$, right?
Just making sure that I am interpreting questions regarding matrix norm correctly.
I am asked to compare the norm of two $3 \times 3$ matrices $A$ and $B$.
The answer is that $$\lVert B \rVert \leqslant \lVert A \rVert, $$ but I notice that every entry of $A$ is bigger than or equal to every entry of $B$. So, the intuition that the norm of A would be bigger leads to the correct answer, in this case. Is this a theorem, though? That would be useful.