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\DeclareMathOperator{\Span}{Span}
\DeclareMathOperator{\leftreg}{L}
\DeclareMathOperator{\rightreg}{R}
\DeclareMathOperator{\matrixring}{M}
\DeclareMathOperator{\GL}{GL}
\DeclareMathOperator{\SL}{SL}
\DeclareMathOperator{\Or}{O}
\DeclareMathOperator{\SO}{SO}
\DeclareMathOperator{\Zntr}{Z}
\DeclareMathOperator{\im}{im}
\DeclareMathOperator{\sgn}{sgn}
\DeclareMathOperator{\trace}{trace}
\DeclareMathOperator{\Stab}{Stab}
\DeclareMathOperator{\Fix}{Fix}
\newcommand{\funcdef}[3]{#1\colon #2\to #3}
\newcommand{\bbrac}[1]{\bigl(#1\bigr)}
\newcommand{\letter}[1]{\mathrm{#1}}
\newcommand{\eqclass}[1]{\left[#1\right]}
\newcommand{\abs}[1]{\left\lvert #1 \right\rvert}
\newcommand{\cardinality}[1]{\abs{#1}}
\newcommand{\grporder}[1]{\cardinality{#1}}
\newcommand{\inv}[2][1]{{#2}^{-{#1}}}
\newcommand{\multunits}[1]{{#1}^\times}
\newcommand{\gen}[1]{\langle#1\rangle}
\newcommand{\cyclesep}{\;\,}
\newcommand{\onecycle}[1]{(\,#1\,)}
\newcommand{\twocycle}[2]{\onecycle{#1{\cyclesep}#2}}
\newcommand{\threecycle}[3]{\twocycle{#1{\cyclesep}#2}{#3}}
\newcommand{\fourcycle}[4]{\threecycle{#1{\cyclesep}#2}{#3}{#4}}
\newcommand{\inducedperm}[1]{\leftreg_{#1}}
\newcommand{\invinducedperm}[1]{\inv{\leftreg}_{#1}}
\newcommand{\inducedpermset}[1]{\inducedperm{#1}}
\newcommand{\commutator}[2]{{#1} {#2} \inv{#1} \inv{#2}}
\newcommand{\commutatorgrp}[1]{\left[ #1, #1 \right]}
\newcommand{\induced}[1]{\widetilde{#1}}
\newcommand{\grpact}[2]{#1(#2)}
\newcommand{\orbit}[1]{\mathcal{O}_{#1}}
\newcommand{\isoto}{\simeq}
\renewcommand{\vec}[1]{\mathbf{#1}}
\newcommand{\zerovec}{\vec{0}}
\newcommand{\trans}[1]{{#1}^{\mathrm{T}}}
\newcommand{\N}{\mathbb{N}}
\newcommand{\Z}{\mathbb{Z}}
\newcommand{\Q}{\mathbb{Q}}
\newcommand{\R}{\mathbb{R}}
\newcommand{\lt}{<}
\newcommand{\gt}{>}
\newcommand{\amp}{&}
\definecolor{fillinmathshade}{gray}{0.9}
\newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}}
\)
AUMAT 229 Activities
September 7, 2022
