Commit a0beae02 by Michael Kohlhase

### replace_atrefi*_with_mtrefi

parent ec8b59b1
 \begin{mhmodnl}[creators=miko]{Minkowski-distance}{en} \begin{definition} Let $\realmorethan{p}1$ be a \trefii[realnumbers]{real}{number}, then we call \atrefii[norm-induced-metric]{metric induced}{induced}{metric} on \mtrefi[norm-induced-metric?induced-metric]{metric induced} on $\ndim\RealNumbers{n}$ by the \mtrefi[pnorm?pnorm]{$\ell_p$-norm} the \defii{Minkowski}{distance} $\MinkowskiDistOp{p}$. We have \[\fundefeq{p,x,y} ... ... @@ -13,7 +13,7 @@ \begin{definition} The \trefi[metric-space]{metric} $\MinkowskiDistOp1$ \atrefii[norm-induced-metric]{induced}{induced}{metric} by the \mtrefi[norm-induced-metric?induced-metric]{induced} by the \trefii[pnorm]{taxicab}{norm} is called the \defii{Manhattan}{distance}, the \defii[name=Manhattan-distance]{rectilinear}{distance}, ... ... @@ -23,7 +23,7 @@ \begin{definition} The \trefi[metric-space]{metric} $\MinkowskiDistOp2$ \atrefii[norm-induced-metric]{induced}{induced}{metric} by the \mtrefi[norm-induced-metric?induced-metric]{induced} by the \mtrefi[pnorm?pnorm]{$\ell_2$-norm} is called the \defii{Euclidean}{distance}. \end{definition} \end{mhmodnl} ... ...
 \begin{mhmodnl}[creators=miko]{inner-product-space}{en} \begin{definition} Let $F$ be the \trefi[field]{field} of \atrefii[realnumbers]{real}{real}{number} or Let $F$ be the \trefi[field]{field} of \mtrefi[realnumbers?real-number]{real} or \trefiis[complexnumbers]{complex}{number}, $V$ a \trefii[vector-space]{vector}{space} over $F$, and $\fun\innerproductOp{V,V}F$ a function with \begin{enumerate} ... ...
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