common.tex

% useful packages
\usepackage{amsfonts,amsmath,amssymb,amsthm,bm,commath,enumerate,graphicx,hyperref,nicefrac,physics,subcaption}

% formatting
\setlength{\parskip}{0.5em}
\setlength{\parindent}{0em}
\usepackage[margin=1.25in]{geometry}
\hypersetup{
    colorlinks=true,
    linktoc=all,
    linkcolor=black,
    urlcolor=blue
}

% shorthand
\DeclareMathOperator*{\argmax}{arg\,max}
\DeclareMathOperator*{\argmin}{arg\,min}
\DeclareMathOperator*{\dom}{dom}
\DeclareMathOperator*{\range}{range}
\DeclareMathOperator*{\diag}{diag}
\DeclareMathOperator*{\Null}{null}
\newcommand{\C}{\mathbb{C}}
\newcommand{\F}{\mathbb{F}}
\newcommand{\N}{\mathbb{N}}
\newcommand{\Q}{\mathbb{Q}}
\newcommand{\R}{\mathbb{R}}
\newcommand{\Z}{\mathbb{Z}}
\newcommand{\calA}{\mathcal{A}}
\newcommand{\calB}{\mathcal{B}}
\newcommand{\calC}{\mathcal{C}}
\newcommand{\calD}{\mathcal{D}}
\newcommand{\calF}{\mathcal{F}}
\newcommand{\calH}{\mathcal{H}}
\newcommand{\calI}{\mathcal{I}}
\newcommand{\calL}{\mathcal{L}}
\newcommand{\calM}{\mathcal{M}}
\newcommand{\calN}{\mathcal{N}}
\newcommand{\calP}{\mathcal{P}}
\newcommand{\calR}{\mathcal{R}}
\newcommand{\calX}{\mathcal{X}}
\renewcommand{\vec}[1]{\mathbf{#1}}
\newcommand{\mat}[1]{\mathbf{#1}}
\newcommand{\matlit}[1]{\begin{bmatrix}#1\end{bmatrix}}
\newcommand{\tran}{^{\!\top\!}}
\newcommand{\inv}{^{-1}}
\newcommand{\halfpow}{^{\frac{1}{2}}}
\newcommand{\neghalfpow}{^{-\frac{1}{2}}}
\renewcommand{\angle}[1]{\langle #1 \rangle}
\newcommand{\bigangle}[1]{\left\langle #1 \right\rangle}
\newcommand{\inner}[2]{\angle{#1, #2}}
\newcommand{\biginner}[2]{\bigangle{#1, #2}}
\renewcommand{\P}{\mathbb{P}}
\newcommand{\pr}[1]{\P(#1)}
\newcommand{\prbig}[1]{\P\big(#1\big)}
\newcommand{\prbigg}[1]{\P\bigg(#1\bigg)}
\newcommand{\prlr}[1]{\P\left(#1\right)}
\newcommand{\comp}{^\text{c}}
\newcommand{\given}{|}
\renewcommand{\ev}[1]{\mathbb{E}[#1]}
\newcommand{\evwrt}[2]{\mathbb{E}_{#1}[#2]}
\renewcommand{\var}[1]{\operatorname{Var}(#1)}
\newcommand{\cov}[2]{\operatorname{Cov}(#1, #2)}
\newcommand{\bigev}[1]{\mathbb{E}\left[#1\right]}
\newcommand{\bigvar}[1]{\operatorname{Var}\left(#1\right)}
\newcommand{\bigcov}[2]{\operatorname{Cov}\left(#1, #2\right)}
\newcommand{\iid}{\overset{\text{iid}}{\sim}}
\newcommand{\bX}{\mathbf{X}}
\newcommand{\term}[1]{\textbf{#1}}
\newcommand{\tab}{\hspace{0.5cm}}
\renewcommand{\a}{\vec{a}}
\renewcommand{\b}{\vec{b}}
\newcommand{\e}{\vec{e}}
\newcommand{\g}{\vec{g}}
\newcommand{\h}{\vec{h}}
\renewcommand{\o}{\vec{o}}
\newcommand{\q}{\vec{q}}
\newcommand{\s}{\vec{s}}
\newcommand{\x}{\vec{x}}
\newcommand{\y}{\vec{y}}
\newcommand{\w}{\vec{w}}
\newcommand{\z}{\vec{z}}
\newcommand{\A}{\mat{A}}
\newcommand{\I}{\mat{I}}
\newcommand{\xye}{\tilde{\x}}
\newcommand{\dotcup}{\mathbin{\dot{\cup}}}
\newcommand{\bigdotcup}{\mathop{\dot{\bigcup}}}

\newtheorem{theorem}{Theorem}
\newtheorem*{theorem*}{Theorem}
\newtheorem{definition}{Definition}
\newtheorem*{definition*}{Definition}
\newtheorem{proposition}{Proposition}
\newtheorem*{proposition*}{Proposition}
\newtheorem{lemma}{Lemma}
\newtheorem*{lemma*}{Lemma}
\newtheorem{corollary}{Corollary}
\newtheorem*{corollary*}{Corollary}
\theoremstyle{remark}
\newtheorem*{note}{Note}
\newtheorem*{example}{Example}