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 differences. I am
Triangle inequality Zero norm iff zero vector We could define a $3$-norm where you sum up all the components cubed and take the cubic root. The infinite norm simply takes the maximum component's absolute value as the norm. The $1$-norm simply works by taking the sum of the absolute value of all components. All these norms fulfill the properties ...
Given a matrix, is the Frobenius norm of that matrix always equal to the 2-norm of it, or are there certain matrices where these two norm methods would produce different results? If they are ident...
What is the difference between the Frobenius norm and the 2-norm of a ...
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 function that has a zero discrete Sobolev norm.
How are $C^0,C^1$ norms defined? I know $L_p,L_\infty$ norms but are the former defined.
Are you sure it holds when there’s no norm? The right hand side of your second “equality” is a scalar.
Not exactly, sorry. I already know it is bounded, all is left is to find/estimate the operator norm more closely
On the other hand, since the square of the norm given by an inner product is a sum of products of linear functionals, the norm arising from an inner product is continuous with respect to $\mathcal L_E$, and hence $\tau_E \subseteq \mathcal L_E$ so that $\tau_E = \mathcal L_E$.