X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=examples.tex;h=0656165d2c7821f1f366cda489bf3dd21f4eaa54;hb=fe30cc3cf8f9a88785d2899d00a727931377bb5d;hp=dde74d0f6997418a8ab283ee1f6fb53452f6a6bf;hpb=8f3a3f952b0e5bd692b9b41d1417c877b0e0425e;p=mjotex.git

diff --git a/examples.tex b/examples.tex
index dde74d0..0656165 100644
--- a/examples.tex
+++ b/examples.tex
@@ -112,6 +112,7 @@
     \begin{equation*}
       \directsummany{k=1}{\infty}{V_{k}} \ne \cartprodmany{k=1}{\infty}{V_{k}}.
     \end{equation*}
+    %
     Here are a few common tuple spaces that should not have a
     superscript when that superscript would be one: $\Nn[1]$,
     $\Zn[1]$, $\Qn[1]$, $\Rn[1]$, $\Cn[1]$. However, if the
@@ -130,8 +131,9 @@
     \begin{equation*}
       \unionmany{k=1}{\infty}{A_{k}} = \intersectmany{k=1}{\infty}{B_{k}}
     \end{equation*}
-
-    Finally, we have the four standard types of intervals in $\Rn[1]$,
+    %
+    The powerset of $X$ displays nicely, as $\powerset{X}$. Finally,
+    we have the four standard types of intervals in $\Rn[1]$,
     %
     \begin{align*}
       \intervaloo{a}{b} &= \setc{ x \in \Rn[1]}{ a < x < b },\\
@@ -171,7 +173,14 @@
   \end{section}
 
   \begin{section}{Font}
-    We can write things like Carathéodory and Güler and $\mathbb{R}$.
+    We can write things like Carathéodory and Güler and
+    $\mathbb{R}$. The PostScript Zapf Chancery font is also available
+    in both upper- and lower-case:
+    %
+    \begin{itemize}
+      \begin{item}$\mathpzc{abcdefghijklmnopqrstuvwxyz}$\end{item}
+      \begin{item}$\mathpzc{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$\end{item}
+    \end{itemize}
   \end{section}
 
   \begin{section}{Linear algebra}
@@ -183,7 +192,11 @@
     $\transpose{L}$. Its trace is $\trace{L}$. Another matrix-specific
     concept is the Moore-Penrose pseudoinverse of $L$, denoted by
     $\pseudoinverse{L}$. Finally, the rank of a matrix $L$ is
-    $\rank{L}$.
+    $\rank{L}$. As far as matrix spaces go, we have the $n$-by-$n$
+    real-symmetric and complex-Hermitian matrices $\Sn$ and $\Hn$
+    respectively; however $\Sn[1]$ and $\Hn[1]$ do not automatically
+    simplify because the ``$n$'' does not indicate the arity of a
+    Cartesian product in this case.
 
     The span of a set $X$ is $\spanof{X}$, and its codimension is
     $\codim{X}$. The projection of $X$ onto $V$ is $\proj{V}{X}$. The