Commit 0b197657 by Michael Kohlhase

### superseded by pnorm.tex

parent a154a1f8
 \begin{mhmodnl}[creators=miko]{pnorm}{en} \begin{definition} Let $\cV$ be a \trefi[realnumbers]{real} \trefii[vector-space]{vector}{space} and $\vbaseset$ its \trefii[vector-space]{base}{set}}, then we call The \defii{Euclidean}{norm} on an \trefii[euclideanspace]{Euclidean}{space} $\ndim{n}\RealNumbers$ is the function $\fundefeq{v}{\euclideannorm{\ntupli{v}1n}}{\sqrt{\Sumfromto{i}1n{\realpower{v_i}2}}}$ The \trefii{Euclidean}{norm} is also called the \defii[name=Euclidean-norm]{Euclidean}{length}, \defii[name=Euclidean-norm]{$L^2$}{distance}, \defii[name=Euclidean-norm]{$L^2$}{norm}, \defii[name=Euclidean-norm]{$\ell^2$}{distance}, or \defii[name=Euclidean-norm]{$\ell^2$}{norm}, \end{definition} \end{mhmodnl} %%% Local Variables: %%% mode: latex %%% TeX-master: t %%% End:
 \begin{modsig}[creators=miko]{euclidean-norm} \gimport[smglom/topology]{euclideanspace} \gimport[smglom/arithmetics]{realarith} \gimport[smglom/arithmetics]{sum} \symdef[name=Euclidean-norm]{euclideannorm}[1]{\left|#1\right|} \symtest{euclideannorm}{\euclideannorm{v}} \end{modsig} %%% Local Variables: %%% mode: latex %%% TeX-master: t %%% End:
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