X-Git-Url: http://gitweb.michael.orlitzky.com/?p=mjotex.git;a=blobdiff_plain;f=examples.tex;h=383cef2b5f9c89889e2d38fbfe4d8d42a5e0e339;hp=d59975eb872bd2f635f9635756518df236e64f74;hb=HEAD;hpb=906dd6be4d6f832228c3d97c9c755fa4fc8d43bf

diff --git a/examples.tex b/examples.tex
index d59975e..383cef2 100644
--- a/examples.tex
+++ b/examples.tex
@@ -39,7 +39,11 @@
 
     If $R$ has a multiplicative identity (that is, a unit) element,
     then that element is denoted by $\unit{R}$. Its additive identity
-    element is $\zero{R}$.
+    element is $\zero{R}$. The stabilizer (or isotropy)
+    subgroup of $G$ that fixes $x$ is $\Stab{G}{x}$.
+
+    If $I$ is an ideal, then $\variety{I}$ is the variety that
+    corresponds to it.
   \end{section}
 
   \begin{section}{Algorithm}
@@ -161,8 +165,12 @@
   \end{section}
 
   \begin{section}{Euclidean Jordan algebras}
-    The Jordan product of $x$ and $y$ in some Euclidean Jordan algebra $V$
-    is $\jp{x}{y}$. The Jordan-automorphism group of $V$ is $\JAut{V}$.
+    The Jordan product of $x$ and $y$ in some Euclidean Jordan algebra
+    $V$ is $\jp{x}{y}$. The Jordan-automorphism group of $V$ is
+    $\JAut{V}$. Two popular operators in an EJA are its quadratic
+    representation and ``left multiplication by'' operator. For a
+    given $x$, they are, respectively, $\quadrepr{x}$ and
+    $\leftmult{x}$.
   \end{section}
 
   \begin{section}{Font}
@@ -209,7 +217,9 @@
 
     The set of all bounded linear operators from $V$ to $W$ is
     $\boundedops[W]{V}$. If $W = V$, then we write $\boundedops{V}$
-    instead.
+    instead. If you have matrices instead, then the general linear
+    group of $n$-by-$n$ matrices with entries in $\mathbb{F}$ is
+    $\GL{n}{\mathbb{F}}$.
 
     If you want to solve a system of equations, try Cramer's
     rule~\cite{ehrenborg}. Or at least the reduced row-echelon form of