Hopefully without getting too complicated, how is a norm different from an absolute value? In context, I am trying to understand relative stability of an algorithim: Using the inequality $\\frac{|...

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 …

In spatial euclidean vector spaces norm is an intuitive concept: It measures the distance from the null vector and from other vectors. The generalization to function spaces is quite a mental leap ...

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 …

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.

Notice that the intersection of all L^p spaces is not necessarily L^infty. Hence, for the argument to work you need a-priori for the L^infty norm to be finite.

All of the norm functions that you stated are non-differentiable somewhere: [$L_0$] This is zero (as you pointed out), but only in places where it isn't interesting.

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 …

Differences between the L1-norm and the L2-norm In mathematics, we prefer it over many other possible norm because it induces the Hilbert Spaces structure on the functions spaces.

Inequalities in $l_p$ norm Ask Question Asked 13 years, 4 months ago Modified 11 years, 3 months ago