From 7a60af0c2fa38f05aecd84b530d3c5b87eaf3de7 Mon Sep 17 00:00:00 2001
From: Michael Orlitzky <michael@orlitzky.com>
Date: Thu, 22 Sep 2016 15:21:46 -0400
Subject: [PATCH] Add my work-in-progress \directsumperp.

---
 examples.tex           | 23 +++++++++++++++++++++++
 mjo-linear_algebra.tex | 16 ++++++++++++++++
 2 files changed, 39 insertions(+)

diff --git a/examples.tex b/examples.tex
index a491bd8..fbbe860 100644
--- a/examples.tex
+++ b/examples.tex
@@ -103,6 +103,29 @@
     The set of all bounded linear operators from $V$ to $W$ is
     $\boundedops[W]{V}$. If $W = V$, then we write $\boundedops{V}$
     instead.
+
+    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
+    writing $\directsumperp{V}{W}$. That operator should survive a
+    display equation, too:
+    %
+    \begin{align*}
+      Z = \directsumperp{V}{W}\\
+      \oplus\oplusperp\oplus\oplusperp
+    \end{align*}
+    %
+    Its form should also survive in different font sizes...
+    \Large
+    \begin{align*}
+      Z = \directsumperp{V}{W}\\
+      \oplus\oplusperp\oplus\oplusperp
+    \end{align*}
+    \Huge
+    \begin{align*}
+      Z = \directsumperp{V}{W}\\
+      \oplus\oplusperp\oplus\oplusperp
+    \end{align*}
+    \normalsize
   \end{section}
 
   \begin{section}{Listing}
diff --git a/mjo-linear_algebra.tex b/mjo-linear_algebra.tex
index ebf4acd..5fce75a 100644
--- a/mjo-linear_algebra.tex
+++ b/mjo-linear_algebra.tex
@@ -71,3 +71,19 @@
     \fi
   }
 }
+
+
+%
+% Orthogonal direct sum.
+%
+% Wasysym contains the \ocircle that we use in \directsumperp.
+\usepackage{wasysym}
+\usepackage{scalerel}
+\DeclareMathOperator{\oplusperp}{\mathbin{
+  \ooalign{
+    $\ocircle$\cr
+    \raisebox{\noexpand{0.65\height}}{${\vstretch{0.5}{\perp}}$}\cr
+  }
+}}
+
+\newcommand*{\directsumperp}[2]{ {#1}\oplusperp{#2} }
-- 
2.44.2