X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo-linear_algebra.tex;h=172010c6a548e4c7dd77a29f67283941152ce356;hb=9585e6612442124b177dd8f46037e30f353369eb;hp=71ab1b61362be810e0a758490641b86a7ae3f52f;hpb=7c7ef6216956f7a5c8bbaf1d9780d2e1aa431342;p=mjotex.git

diff --git a/mjo-linear_algebra.tex b/mjo-linear_algebra.tex
index 71ab1b6..172010c 100644
--- a/mjo-linear_algebra.tex
+++ b/mjo-linear_algebra.tex
@@ -14,7 +14,7 @@
 \newcommand*{\norm}[1]{\left\lVert{#1}\right\rVert}
 
 % The inner product between its two arguments.
-\newcommand*{\ip}[2]{\langle{#1},{#2}\rangle}
+\newcommand*{\ip}[2]{\left\langle{#1},{#2}\right\rangle}
 
 % The tensor product of its two arguments.
 \newcommand*{\tp}[2]{ {#1}\otimes{#2} }
@@ -25,7 +25,11 @@
 \newcommand*{\kp}[2]{ {#1}\odot{#2} }
 
 % The adjoint of a linear operator.
-\newcommand*{\adjoint}[1]{ {#1}^{*} }
+\newcommand*{\adjoint}[1]{ #1^{*} }
+
+% The ``transpose'' of a linear operator; namely, the adjoint, but
+% specialized to real matrices.
+\newcommand*{\transpose}[1]{ #1^{T} }
 
 % The ``span of'' operator. The name \span is already taken.
 \newcommand*{\spanof}[1]{ \operatorname{span}\of{{#1}} }