\documentclass[a4paper,ngerman]{scrartcl}
\usepackage[ngerman]{babel}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{hyperref}
\usepackage[pdftex]{graphicx}
\usepackage[babel,german=quotes]{csquotes}
\usepackage{amsmath,amssymb,amsthm}
\usepackage{stmaryrd}
\usepackage{bbm}
\usepackage{tikz}

\newcommand{\punkte}[1]{\hspace*{\fill}\textit{\mbox{(#1)}}\par}

\newtheorem{satzthm}{Satz}
\newcommand{\satz}[2]{\begin{satzthm}[#1]#2\end{satzthm}}

\newtheorem{folgthm}{Folgerung}
\newcommand{\folgerung}[2]{\begin{folgthm}[#1]#2\end{folgthm}}

\newtheorem{defthm}{Definition}
\newcommand{\defin}[2]{\begin{defthm}[#1]#2\end{defthm}}

\newtheorem{bemthm}{Bemerkung}
\newcommand{\bem}[1]{\begin{bemthm}#1\end{bemthm}}

\newtheorem{bspthm}{Beispiel}
\newcommand{\bsp}[1]{\begin{bspthm}#1\end{bspthm}}

\newcommand{\bew}[1]{\begin{proof}#1\end{proof}}

\def\K{\ensuremath{\mathbbm{K}}}
\def\C{\ensuremath{\mathbbm{C}}}
\def\R{\ensuremath{\mathbbm{R}}}
\def\Q{\ensuremath{\mathbbm{Q}}}
\def\Z{\ensuremath{\mathbbm{Z}}}
\def\N{\ensuremath{\mathbbm{N}}}

\newcommand{\de}[1]{\ensuremath{\mathrm{d}#1}}
\newcommand{\De}[1]{\ensuremath{\mathrm{D}_{#1}}}
\DeclareMathOperator{\gradop}{grad}
\DeclareMathOperator{\divop}{div}
\DeclareMathOperator{\rotop}{rot}

\def\eps{\ensuremath{\varepsilon}}

\DeclareMathOperator{\sgn}{sgn}
\DeclareMathOperator{\sign}{sign}
\DeclareMathOperator{\artanh}{artanh}
\DeclareMathOperator{\arsinh}{arsinh}
\DeclareMathOperator{\arcosh}{arcosh}
\DeclareMathOperator{\tr}{tr}
\DeclareMathOperator{\charop}{char}
\DeclareMathOperator{\id}{Id}
\DeclareMathOperator{\rg}{rg}
\DeclareMathOperator{\aut}{Aut}
\DeclareMathOperator{\GL}{GL}
\DeclareMathOperator{\Aff}{Aff}
\DeclareMathOperator{\affh}{aff}
\DeclareMathOperator{\inner}{int}
\DeclareMathOperator{\relinner}{relint}
\DeclareMathOperator{\diam}{diam}
\DeclareMathOperator{\vol}{vol}
\DeclareMathOperator{\convh}{conv}
\DeclareMathOperator{\bild}{img}
\DeclareMathOperator{\oKugel}{B}
\DeclareMathOperator{\card}{card}
\newcommand{\linh}[1]{\ensuremath{\operatorname{span}\left\{#1\right\}}}
\newcommand{\eig}[2]{\ensuremath{\operatorname{Eig}_{#1}\left(#2\right)}}
\newcommand{\alg}[2]{\ensuremath{\operatorname{alg}_{#1}\left(#2\right)}}
\newcommand{\geo}[2]{\ensuremath{\operatorname{geo}_{#1}\left(#2\right)}}
\newcommand{\mat}[3]{\ensuremath{\operatorname{Mat}\left(#1, #2, #3\right)}}
\newcommand{\Min}[2]{\ensuremath{\operatorname{Min}_{#1}\left(#2\right)}}

\DeclareMathOperator{\cov}{cov}

\newcommand{\ol}[1]{\ensuremath{\overline{#1}}}
\newcommand{\opfeil}[1]{\ensuremath{\overrightarrow{#1}}}
\def\folgt{\ensuremath{\Rightarrow}}
\def\gdw{\ensuremath{\Leftrightarrow}}
\newcommand{\mmat}[1]{\ensuremath{\begin{matrix}#1\end{matrix}}}
\newcommand{\pmat}[1]{\ensuremath{\begin{pmatrix}#1\end{pmatrix}}}
\newcommand{\bmat}[1]{\ensuremath{\begin{bmatrix}#1\end{bmatrix}}}
\newcommand{\vmat}[1]{\ensuremath{\begin{vmatrix}#1\end{vmatrix}}}
