For example, in matlab, norm (A,2) gives you induced 2-norm, which they simply call the 2-norm. So in that sense, the answer to your question is that the (induced) matrix 2-norm is $\le$ than Frobenius …

Jan 24, 2013 · In number theory, the "norm" is the determinant of this matrix. In that sense, unlike in analysis, the norm can be thought of as an area rather than a length, because the determinant can …

Feb 6, 2021 · I am not a mathematics student but somehow have to know about L1 and L2 norms. I am looking for some appropriate sources to learn these things and know they work and what are their …

Jul 5, 2024 · Are you sure it holds when there’s no norm? The right hand side of your second “equality” is a scalar.

The operator norm is a matrix/operator norm associated with a vector norm. It is defined as $||A||_ {\text {OP}} = \text {sup}_ {x \neq 0} \frac {|A x|_n} {|x|}$ and different for each vector norm. In case of the …

Feb 10, 2026 · Yes, as indicated by daw, because your discrete Sobolev norm only includes the values of the function evaluated at the discrete mesh points, it is always possible to construct a nonzero …

Jan 25, 2022 · How are $C^0,C^1$ norms defined? I know $L_p,L_\\infty$ norms but are the former defined.

Dec 17, 2017 · I've read the Uniform Norm Wikipedia page, but my most of it went over my head. What is the sup-norm in simple and / or intuitive terms? Are there any good examples which illustrate it?

Mar 2, 2024 · Not exactly, sorry. I already know it is bounded, all is left is to find/estimate the operator norm more closely

Okay, I'll try to prove it. Your answer is very helpful, thanks again. Do you happen to know a reference (where the norm is explicitly explained)?