% specialized to real matrices.
\newcommand*{\transpose}[1]{ #1^{T} }
+% The Moore-Penrose (or any other, I guess) pseudo-inverse of its
+% sole argument.
+\newcommand*{\pseudoinverse}[1]{ #1^{+} }
+
% The trace of an operator.
\newcommand*{\trace}[1]{ \operatorname{trace}\of{{#1}} }
\DeclareMathOperator{\oplusperp}{\mathbin{
\ooalign{
$\ocircle$\cr
- \raisebox{0.65\height}{$\clipbox{0pt 0pt 0pt 0.5\height}{$\perp$}$}\cr
+ \raisebox{0.625\height}{$\clipbox{0pt 0pt 0pt 0.5\height}{$\perp$}$}\cr
}
}}