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 …

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 …

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 …

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 …

Apr 22, 2016 · The original question was asking about a matrix H and a matrix A, so presumably we are talking about the operator norm. The selected answer doesn't parse with the definitions …

Aug 16, 2013 · What norm are you using in $H^1$? or better saying what is the definition of $\|\cdot\|_ {H^1}$ for you?

This proof is really a way of saying that the topology induced by a norm on a finite-dimensional vector space is the same as the topology defined by open half-spaces; in particular, all norms …

Dec 23, 2016 · However, this post seems to shatter my assumption: 2-norm vs operator norm. Upon further examination, it seems that the operator norm and matrix norm only coincide (=) …

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

May 23, 2017 · I know the definitions of the $1$ and $2$ norm, and, numerically the inequality seems obvious, although I don't know where to start rigorously. Thank you.