\newcommand{\R}{\mathbb{R}}
\newcommand{\C}{\mathbb{C}}
\newcommand{\N}{\mathbb{N}}
\newcommand{\K}{\mathbb{K}}
\newcommand{\Q}{\mathbb{Q}}
\newcommand{\Z}{\mathbb{Z}}

% an interval
\newcommand{\J}{\mathcal{J}}

\newcommand{\powerset}[1]{\mathcal{P}(#1)}
\newcommand{\skp}[1]{\langle #1 \rangle}
\newcommand{\restrictedto}[2]{{\left.\kern-\nulldelimiterspace #1 \vphantom{\big|} \right|_{#2}}}
\newcommand{\transpose}[1]{#1^\mathsf{T}}

\newcommand{\spacing}{\vspace{2mm}}