Commit a0beae02 authored by Michael Kohlhase's avatar 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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