From cab35094298c00d10035e926b64ff69df33393a5 Mon Sep 17 00:00:00 2001
From: Michael Orlitzky <michael@orlitzky.com>
Date: Sat, 13 Feb 2021 18:14:05 -0500
Subject: [PATCH] mjo-linear_algebra.tex: add \rref{} macro.

---
 examples.tex           |  3 ++-
 mjo-linear_algebra.tex | 10 ++++++++++
 2 files changed, 12 insertions(+), 1 deletion(-)

diff --git a/examples.tex b/examples.tex
index 015c5fd..babc886 100644
--- a/examples.tex
+++ b/examples.tex
@@ -203,7 +203,8 @@
     instead.
 
     If you want to solve a system of equations, try Cramer's
-    rule~\cite{ehrenborg}.
+    rule~\cite{ehrenborg}. Or at least the reduced row-echelon form of
+    the matrix, $\rref{A}$.
 
     The direct sum of $V$ and $W$ is $\directsum{V}{W}$, of course,
     but what if $W = V^{\perp}$? Then we wish to indicate that fact by
diff --git a/mjo-linear_algebra.tex b/mjo-linear_algebra.tex
index a534523..7f2484a 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}} }
 
-- 
2.43.2