X-Git-Url: http://gitweb.michael.orlitzky.com/?p=mjotex.git;a=blobdiff_plain;f=mjo-linear_algebra.tex;h=7f2484a546ef750977ca2b4c1ab7ae451a66f122;hp=c57e9b9534309d70d760540ba464b94511a1f085;hb=HEAD;hpb=10b83af54da036b9f3122b5e82b18816c5acf386

diff --git a/mjo-linear_algebra.tex b/mjo-linear_algebra.tex
index c57e9b9..5f25544 100644
--- a/mjo-linear_algebra.tex
+++ b/mjo-linear_algebra.tex
@@ -89,6 +89,16 @@
   }
 \fi
 
+% The reduced row-echelon form of its argument, a matrix.
+\newcommand*{\rref}[1]{\operatorname{rref}\of{#1}}
+\ifdefined\newglossaryentry
+  \newglossaryentry{rref}{
+    name={\ensuremath{\rref{A}}},
+    description={the reduced row-echelon form of $A$},
+    sort=r
+  }
+\fi
+
 % The ``Automorphism group of'' operator.
 \newcommand*{\Aut}[1]{ \operatorname{Aut}\of{{#1}} }
 
@@ -151,7 +161,9 @@
 
 % The space of complex Hermitian n-by-n matrices. Does not reduce to
 % merely "H" when n=1 since H^{n} does not mean an n-fold cartesian
-% product of H^{1}.
+% product of H^{1}. The field may also be given rather than assumed
+% to be complex; for example \Hn[3]\of{\mathbb{O}} might denote the
+% 3-by-3 Hermitian matrices with octonion entries.
 \newcommand*{\Hn}[1][n]{ \mathcal{H}^{#1} }
 \ifdefined\newglossaryentry
   \newglossaryentry{Hn}{
@@ -162,4 +174,8 @@
 \fi
 
 
+% The general linear group of square matrices whose size is the first
+% argument and whose entries come from the second argument.
+\newcommand*{\GL}[2]{\operatorname{GL}_{#1}\of{#2}}
+
 \fi