From daa8ca73cd506b68668cad9e78516fbb7c779954 Mon Sep 17 00:00:00 2001
From: Michael Orlitzky <michael@orlitzky.com>
Date: Sun, 24 Nov 2024 11:03:54 -0500
Subject: [PATCH] {examples,mjo-linear_algebra}.tex: add \Isom for isometries

---
 examples.tex           |  7 +++++--
 mjo-linear_algebra.tex | 29 +++++++++++++++++++++++++++++
 2 files changed, 34 insertions(+), 2 deletions(-)

diff --git a/examples.tex b/examples.tex
index 9096b70..accec5d 100644
--- a/examples.tex
+++ b/examples.tex
@@ -254,8 +254,11 @@
     \end{align*}
     \normalsize
 
-    If $V$ is an algebra, then $\Der{V}$ is the space of all
-    (linear) derivations on $V$.
+    If $V$ is an algebra, then $\Der{V}$ is the space of all (linear)
+    derivations on $V$. We also have the group of isometries on $V$,
+    if $V$ has a metric: $\Isom{V}$. More generally, if $V$ and $W$
+    are both metric spaces, then we can represent the isometries from
+    one to the other by $\Isom[W]{V}$.
   \end{section}
 
   \begin{section}{Listing}
diff --git a/mjo-linear_algebra.tex b/mjo-linear_algebra.tex
index 062121f..32d4d6c 100644
--- a/mjo-linear_algebra.tex
+++ b/mjo-linear_algebra.tex
@@ -196,4 +196,33 @@
   }
 \fi
 
+
+% The set of all isometries from its first argument to its second
+% (optional) argument, both assumed to be at least normed spaces, and
+% more likely Hilbert spaces. The norms are implicit, i.e. not
+% included in the arguments. If the optional argument is omitted, you
+% get the isometries from the first argument to itself AKA its
+% isometry group.
+\newcommand*{\Isom}[2][]{
+  \operatorname{Isom}\of{ {#2}
+    \if\relax\detokenize{#1}\relax
+      {}%
+    \else
+      {,{#1}}%
+    \fi
+  }
+}
+\ifdefined\newglossaryentry
+  \newglossaryentry{Isom}{
+    name={\ensuremath{\Isom{V}}},
+    description={the group of isometries on $V$},
+    sort=Isom
+  }
+  \newglossaryentry{Isom2}{
+    name={\ensuremath{\Isom[W]{V}}},
+    description={the set of isometries from $V$ to $W$},
+    sort=Isom
+  }
+\fi
+
 \fi
-- 
2.44.2