\[
\def\R{{\mathbb R}}
\def\P{{\mathbb P}}
\def\B{{\mathcal B}}
\def\C{{\mathcal C}}
\def\S{{\mathcal S}}
\def\b{{\mathbf{b}}}
\def\a{{\mathbf{a}}}
\def\c{{\mathbf{c}}}
\def\x{{\mathbf{x}}}
\def\y{{\mathbf{y}}}
\def\u{{\mathbf{u}}}
\def\v{{\mathbf{v}}}
\def\w{{\mathbf{w}}}
\def\z{{\mathbf{z}}}
\def\e{{\mathbf{e}}}
\def\r{{\mathbf{r}}}
\def\M{{\mathcal{M}}}
\DeclareMathOperator{\null}{Nul}
\DeclareMathOperator{\span}{Span}
\DeclareMathOperator{\dim}{dim}
\DeclareMathOperator{\proj}{proj}
\DeclareMathOperator{\row}{Row}
\DeclareMathOperator{\col}{Col}
\DeclareMathOperator{\trace}{trace}
\newcommand{\set}[1]{\left\{ {#1} \right\}}
\newcommand{\setof}[2]{{\left\{#1\,\colon\,#2\right\}}}
\newcommand{\norm}[1]{{\left|\! \left| #1 \right| \! \right|}}
\newcommand{\ip}[1]{{\left\langle #1 \right\rangle}}
\newcommand{\tr}[1]{{{#1}^\textsf{T}}}
\]
