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Dec 17, 2017 · For finite vectors $x$, the sup norm of $x$ is the greatest element of $x$ (greatest in absolute value of course to make complex elements ordered and to not distinguish the sign). Example: $(1,-1,2i)$ has greatest element $|2i|=2$.
In mathematics, a norm is a function from a real or complex vector space to the non-negative real numbers that behaves in certain ways like the distance from the origin: it commutes with scaling, obeys a form of the triangle inequality, and is zero only at the origin. In particular, the Euclidean distance in a Euclidean space is defined by a ...
May 28, 2023 · Definition 9.2.1. Let \(V \) be a vector space over \(\mathbb{F}\). A map \begin{equation*} \begin{split} \norm{\cdot} : V &\to \mathbb{R}\\ v &\mapsto \norm{v} \end{split} \end{equation*} is a norm on \(V \) if the following three conditions are satisfied. Positive definiteness: \(\norm{v}=0 \) if and only if \(v=0\);
\[|x|=\sqrt{\sum_{k=1}^{n}\left|x_{k}\right|^{2}},\] where \(x=\left(x_{1}, \ldots, x_{n}\right) .\) This is the so-called standard norm, usually presupposed in \(E^{n}\left(C^{n}\right) .\) (B) One can also define other, "nonstandard," norms on \(E^{n}\) and \(C^{n} .\) For example, fix some real \(p \geq 1\) and put
Using the basis to identify V with F n, we can define the sup norm of any vector (a 1, a 2, … a n ) as max i | a i | . You should verify that this is indeed a norm on F n .
Jun 29, 2022 · We often times need to measure the size of a vector, and in order to do this we use a function called norm, usually denoted by L^p, which looks as so: The norm of a vector x measures the...
4 days ago · The norm of a complex number, 2-norm of a vector, or 2-norm of a (numeric) matrix is returned by Norm [expr]. Furthermore, the generalized -norm of a vector or (numeric) matrix is returned by Norm [expr, p].
