X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo-linear_algebra.tex;h=172010c6a548e4c7dd77a29f67283941152ce356;hb=9585e6612442124b177dd8f46037e30f353369eb;hp=e11a9458843f56484a08538111063f3de869c9f8;hpb=38147a40c34416d5dbd87f44d8786e3dd73a132f;p=mjotex.git

diff --git a/mjo-linear_algebra.tex b/mjo-linear_algebra.tex
index e11a945..172010c 100644
--- a/mjo-linear_algebra.tex
+++ b/mjo-linear_algebra.tex
@@ -14,11 +14,23 @@
 \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} }
 
+% The Kronecker product of its two arguments. The usual notation for
+% this is the same as the tensor product notation used for \tp, but
+% that leads to confusion because the two definitions may not agree.
+\newcommand*{\kp}[2]{ {#1}\odot{#2} }
+
+% The adjoint of a linear operator.
+\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}} }