% 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}} }