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commands.sty
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commands.sty
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\NeedsTeXFormat{LaTeX2e}
\ProvidesPackage{commands}[2017/10/25 Math macros]
\RequirePackage{etoolbox}
\newtoggle{isdraft}
\DeclareOption{draft}{\toggletrue{isdraft}}
\ProcessOptions\relax
\newcommand{\todo}[1]{
\iftoggle{isdraft}{
\vspace{5 mm}\par \noindent \marginpar{\textsc{ToDo}}
\framebox{\begin{minipage}[c]{0.95 \columnwidth} \tt #1
\end{minipage}}\vspace{5 mm}\par}{}}
\newcommand{\propchange}[1]{
\iftoggle{isdraft}{
\textcolor{blue}{#1}}{#1}}
\newcommand{\propdelete}[2]{
\iftoggle{isdraft}{
\textcolor{blue}{\sout{#1} {#2}}}{}}
\newtheorem{theorem}{Theorem}
\numberwithin{theorem}{section}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{coro}[theorem]{Corollary}
\newtheorem{remark}[theorem]{Remark}
\def\qed{\rule[0pt]{5pt}{5pt}\par\medskip}
\renewcommand{\qedhere}{\hfill ~\qed}
\renewenvironment{proof}{{\noindent\bf Proof.}}{\qedhere}
\newcommand{\minimize}{\mbox{minimize}}
\newcommand{\maximize}{\mbox{maximize}}
\newcommand{\st}{\mbox{subject to}}
\newcommand{\statespace}[4]{\left[ \begin{array}{c|c} #1 & #2 \\ \hline\rule{0pt}{2.6ex} #3 & #4 \end{array} \right]}
\newcommand{\tf}[1]{\mathbf{#1}}
\newcommand{\Ah}{\widehat{A}}
\newcommand{\Ahat}{\Ah}
\newcommand{\Bhat}{\Bh}
\newcommand{\Bh}{\widehat{B}}
\newcommand{\Kh}{\widehat{K}}
\newcommand{\Jh}{\widehat{J}}
\newcommand{\Phixh}{\hat{\tf \Phi}_x}
\newcommand{\Phiuh}{\hat{\tf \Phi}_u}
\newcommand{\Dh}{\hat{\tf{\Delta}}}
\newcommand{\trueA}{A}
\newcommand{\trueB}{B}
\newcommand{\trueK}{\tf K_\star}
\newcommand{\A}{\mathcal{A}}
\newcommand{\B}{\mathcal{B}}
\newcommand{\Qq}{\mathcal{Q}}
\newcommand{\Ss}{\mathcal{S}}
\newcommand{\Ahh}{\hat{\A}}
\newcommand{\Bhh}{\hat{\B}}
\newcommand{\DA}{\mathcal{D}_{\A}}
\newcommand{\DB}{\mathcal{D}_{\B}}
\DeclareMathOperator*{\argmin}{arg\!\min}
\DeclareMathOperator*{\argmax}{arg\!\max}
\DeclareMathOperator*{\sgn}{sgn}
\DeclareMathOperator*{\supp}{supp}
\DeclareMathOperator*{\rank}{rank}
\DeclareMathOperator*{\diag}{diag}
\DeclareMathOperator*{\Tr}{\mathbf{Tr}}
\DeclareMathOperator*{\image}{Im}
\DeclareMathOperator*{\nullspace}{Kern}
\DeclareMathOperator*{\rowspace}{RS}
\DeclareMathOperator*{\colspace}{CS}
\DeclareMathOperator*{\dom}{dom}
\DeclareMathOperator*{\closure}{cl}
\DeclareMathOperator*{\vol}{vol}
\DeclareMathOperator*{\Span}{span}
\DeclareMathOperator*{\polylog}{polylog}
\DeclareMathOperator*{\Band}{Band}
\newcommand{\grad}{\mathrm{grad}}
\newcommand{\bias}{\mathrm{Bias}}
\newcommand{\var}{\mathrm{Var}}
\newcommand{\Acal}{\ensuremath{\mathcal{A}}}
\newcommand{\Cset}{\ensuremath{\mathcal{C}}}
\newcommand{\X}{\ensuremath{\mathcal{X}}}
\newcommand{\Y}{\ensuremath{\mathcal{Y}}}
\newcommand{\Z}{\ensuremath{\mathcal{Z}}}
\newcommand{\R}{\ensuremath{\mathbb{R}}}
\newcommand{\C}{\ensuremath{\mathbb{C}}}
\newcommand{\Bcal}{\ensuremath{\mathcal{B}}}
\newcommand{\G}{\ensuremath{\mathcal{G}}}
\newcommand{\Q}{\ensuremath{\mathbb{Q}}}
\newcommand{\N}{\ensuremath{\mathbb{N}}}
\newcommand{\F}{\ensuremath{\mathcal{F}}}
\newcommand{\I}{\ensuremath{\mathcal{I}}}
\newcommand{\Set}{\ensuremath{\mathcal{S}}}
\newcommand{\Hyp}{\ensuremath{\mathcal{H}}}
\newcommand{\Loss}{\ensuremath{\mathcal{L}}}
\newcommand{\Lagrange}{\ensuremath{\mathcal{L}}}
\newcommand{\norm}[1]{\lVert #1 \rVert}
\newcommand{\bignorm}[1]{\left\lVert #1 \right\rVert}
\newcommand{\twonorm}[1]{\lVert #1 \rVert_{2}}
\newcommand{\bigtwonorm}[1]{\left\lVert #1 \right\rVert_{2}}
\newcommand{\spectralnorm}[1]{\twonorm{#1}}
\newcommand{\bigspectralnorm}[1]{\bigtwonorm{#1}}
\newcommand{\maxnorm}[1]{\lVert #1 \rVert_{\infty}}
\newcommand{\onenorm}[1]{\left\lVert #1 \right\rVert_{1}}
\newcommand{\mb}[1]{\mathbf{#1}}
\newcommand{\ip}[2]{\ensuremath{\langle #1, #2 \rangle}}
\newcommand{\PD}[2]{\ensuremath{\frac{\partial #1}{\partial #2}}}
\newcommand{\Var}{\mathrm{Var}}
\newcommand{\E}{\mathbb{E}}
\newcommand{\abs}[1]{\ensuremath{| #1 |}}
\newcommand{\bigabs}[1]{\ensuremath{\left| #1 \right|}}
\newcommand{\floor}[1]{\lfloor #1 \rfloor}
\newcommand{\ceil}[1]{\lceil #1 \rceil}
\newcommand{\Normal}{\mathcal{N}}
\newcommand{\rdraw}{\xleftarrow{\$}}
\newcommand{\ind}{\mathbf{1}}
\renewcommand{\vec}{\mathrm{vec}}
\newcommand{\Sym}{\mathbf{S}}
\newcommand{\Toep}{\mathrm{Toep}}
\newcommand{\leb}{\mu}
\renewcommand{\Pr}{\mathbb{P}}
\newcommand{\T}{*}
\newcommand{\tp}{\mathsf{T}}
\newcommand{\Ncal}{\mathcal{N}}
\newcommand{\vecx}{{x}}
\newcommand{\vecw}{{w}}
\newcommand{\vecu}{{u}}
\newcommand{\PP}{\mathbb{P}}
\newcommand{\RR}{\mathbb{R}}
\newcommand{\Res}[1]{\mathfrak{R}_{#1}}
\newcommand{\Rt}{\tf{\tilde{R}}}
\newcommand{\Mt}{\tf{\tilde{M}}}
\newcommand{\Nt}{\tf{\tilde{N}}}
\newcommand{\Lt}{\tf{\tilde{L}}}
\newcommand{\Kt}{\tf{\tilde{K}}}
\newcommand{\Pt}{\tf{\tilde{P}}}
\newcommand{\Gt}{\tf{\tilde{G}}}
\newcommand{\gt}{\tilde{g}}
\newcommand{\Ro}{\tf{{R}}_0}
\newcommand{\Mo}{\tf{{M}}_0}
\newcommand{\No}{\tf{{N}}_0}
\newcommand{\Lo}{\tf{{L}}_0}
\newcommand{\Ko}{\tf{{K}}_0}
\newcommand{\Rh}{\tf{\hat{R}}}
\newcommand{\Mh}{\tf{\hat{M}}}
\newcommand{\Nh}{\tf{\hat{N}}}
\newcommand{\Lh}{\tf{\hat{L}}}
\newcommand{\wh}{\hat{w}}
\newcommand{\Thetat}{\tf{\widetilde{\Theta}}}
\newcommand{\Thetah}{\tf{\widehat{\Theta}}}
\newcommand{\Thetamat}{\begin{bmatrix} \tf R & \tf N \\ \tf M & \tf L \end{bmatrix}}
\newcommand{\Thetatmat}{\begin{bmatrix} \Rt & \Nt \\ \Mt & \Lt \end{bmatrix}}
\newcommand{\Thetahmat}{\begin{bmatrix} \Rh & \Nh \\ \Mh & \Lh \end{bmatrix}}
\newcommand{\statedim}{n}
\newcommand{\inputdim}{p}
\newcommand{\hinf}{\mathcal{H}_\infty}
\newcommand{\htwo}{\mathcal{H}_2}
\newcommand{\RHinf}{\mathcal{RH}_\infty}
\newcommand{\ltwonorm}[1]{\| #1 \|_2}
\newcommand{\hinfnorm}[1]{\| #1 \|_{\hinf}}
\newcommand{\iid}{\stackrel{\mathclap{\text{\scriptsize{ \tiny i.i.d.}}}}{\sim}}
\newcommand{\opt}{\mathrm{opt}}