Might be an odd question, but why the l2 norm of a matrix is defined the way it is defined? Given the definition,
$$\|A\|_2 = \text{max} \frac{\|Ax\|_2}{\|x\|_2}$$
Specifically:
- why is it the maximum of the argument rather than the minimum, for example?
- Also, why do we divide by the l2 norm of a vector?
- Also, why do we need a vector to define a norm of a matrix at all?
I'm not a mathematician, so if these questions seem weird, sorry in advance.
Thanks.