X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=examples.tex;h=af11de8284796dd1125b0ee8443cd9b1a9c617ca;hb=83458c3f65b80a7897ced0553804b38f4872fcb6;hp=cd615de16cbab3fc8381aac6aeb4039d945f5601;hpb=123eb0365b7a38288f0cd80a0c70b203b8ff33fd;p=mjotex.git

diff --git a/examples.tex b/examples.tex
index cd615de..af11de8 100644
--- a/examples.tex
+++ b/examples.tex
@@ -192,7 +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
@@ -258,11 +262,6 @@
     system to test them.
   \end{section}
 
-  \begin{section}{Miscellaneous}
-    The cardinality of the set $X \coloneqq \set{1,2,3}$ is $\card{X}
-    = 3$.
-  \end{section}
-
   \begin{section}{Proof by cases}
 
     \begin{proposition}
@@ -309,6 +308,11 @@
     \renewcommand{\baselinestretch}{1}
   \end{section}
 
+  \begin{section}{Set theory}
+    The cardinality of the set $X \coloneqq \set{1,2,3}$ is $\card{X}
+    = 3$.
+  \end{section}
+
   \begin{section}{Theorems}
     \begin{corollary}
       The