X-Git-Url: http://gitweb.michael.orlitzky.com/?p=mjotex.git;a=blobdiff_plain;f=mjo-linear_algebra.tex;h=048022935b681bfe5f0d0c04366f7fadcb6383d2;hp=5fce75a403b83ace1b686c622f05ea24e1248363;hb=5c4f67545f0988d065f1d52f90eed9233562c9fc;hpb=7a60af0c2fa38f05aecd84b530d3c5b87eaf3de7

diff --git a/mjo-linear_algebra.tex b/mjo-linear_algebra.tex
index 5fce75a..0480229 100644
--- a/mjo-linear_algebra.tex
+++ b/mjo-linear_algebra.tex
@@ -5,6 +5,12 @@
 % Needed for \lvert, \rVert, etc. and \operatorname.
 \usepackage{amsmath}
 
+% Wasysym contains the \ocircle that we use in \directsumperp.
+\usepackage{wasysym}
+
+% Part of the adjustbox package; needed to clip the \perp sign.
+\usepackage{trimclip}
+
 \input{mjo-common}
 
 % Absolute value (modulus) of a scalar.
@@ -76,14 +82,16 @@
 %
 % Orthogonal direct sum.
 %
-% Wasysym contains the \ocircle that we use in \directsumperp.
-\usepackage{wasysym}
-\usepackage{scalerel}
+% First declare my ``perp in a circle'' operator, which is meant to be
+% like an \obot or an \operp except has the correct weight circle. It's
+% achieved by overlaying an \ocircle with a \perp, but only after we
+% clip off the top half of the \perp sign and shift it up.
 \DeclareMathOperator{\oplusperp}{\mathbin{
   \ooalign{
     $\ocircle$\cr
-    \raisebox{\noexpand{0.65\height}}{${\vstretch{0.5}{\perp}}$}\cr
+    \raisebox{0.65\height}{$\clipbox{0pt 0pt 0pt 0.5\height}{$\perp$}$}\cr
   }
 }}
 
+% Now declare an orthogonal direct sum in terms of \oplusperp.
 \newcommand*{\directsumperp}[2]{ {#1}\oplusperp{#2} }