X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo-linear_algebra.tex;h=5fce75a403b83ace1b686c622f05ea24e1248363;hb=7a60af0c2fa38f05aecd84b530d3c5b87eaf3de7;hp=172010c6a548e4c7dd77a29f67283941152ce356;hpb=9585e6612442124b177dd8f46037e30f353369eb;p=mjotex.git

diff --git a/mjo-linear_algebra.tex b/mjo-linear_algebra.tex
index 172010c..5fce75a 100644
--- a/mjo-linear_algebra.tex
+++ b/mjo-linear_algebra.tex
@@ -7,7 +7,7 @@
 
 \input{mjo-common}
 
-% Absolute value (modulis) of a scalar.
+% Absolute value (modulus) of a scalar.
 \newcommand*{\abs}[1]{\left\lvert{#1}\right\rvert}
 
 % Norm of a vector.
@@ -31,15 +31,15 @@
 % specialized to real matrices.
 \newcommand*{\transpose}[1]{ #1^{T} }
 
+% The trace of an operator.
+\newcommand*{\trace}[1]{ \operatorname{trace}\of{{#1}} }
+
 % The ``span of'' operator. The name \span is already taken.
 \newcommand*{\spanof}[1]{ \operatorname{span}\of{{#1}} }
 
 % The ``co-dimension of'' operator.
 \newcommand*{\codim}{ \operatorname{codim} }
 
-% The trace of an operator.
-\newcommand*{\trace}[1]{ \operatorname{trace}\of{{#1}} }
-
 % The orthogonal projection of its second argument onto the first.
 \newcommand*{\proj}[2] { \operatorname{proj}\of{#1, #2} }
 
@@ -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} }