Add \adjoint and \kp (nonstandard notation for Kronecker product) commands.

diff --git a/mjo-linear_algebra.tex b/mjo-linear_algebra.tex
index e11a9458843f56484a08538111063f3de869c9f8..71ab1b61362be810e0a758490641b86a7ae3f52f 100644 (file)
--- a/mjo-linear_algebra.tex
+++ b/mjo-linear_algebra.tex
@@ -19,6 +19,14 @@
 % 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 ``span of'' operator. The name \span is already taken.
 \newcommand*{\spanof}[1]{ \operatorname{span}\of{{#1}} }