+\newcommand*{\matricize}[1]{ \operatorname{mat}\of{{#1}} }
+
+% An inline column vector, with parentheses and a transpose operator.
+\newcommand*{\colvec}[1]{ \left({#1}\right)^{T} }
+
+% Bounded linear operators on some space. The required argument is the
+% domain of those operators, and the optional argument is the
+% codomain. If the optional argument is omitted, the required argument
+% is used for both.
+\newcommand*{\boundedops}[2][]{
+ \mathcal{B}\of{ {#2}
+ \if\relax\detokenize{#1}\relax
+ {}%
+ \else
+ {,{#1}}%
+ \fi
+ }
+}
+
+
+%
+% Orthogonal direct sum.
+%
+% Wasysym contains the \ocircle that we use in \directsumperp.
+\usepackage{wasysym}
+\usepackage{scalerel}
+\DeclareMathOperator{\oplusperp}{\mathbin{
+ \ooalign{
+ $\ocircle$\cr
+ \raisebox{\noexpand{0.65\height}}{${\vstretch{0.5}{\perp}}$}\cr
+ }
+}}