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+% About: Macros for Vector, Matrix, Tensor, Math Operator and Misc
+% Author: Jingxuan Yang
+
+% vectors
+\newcommand{\va}{\bm{a}} \newcommand{\vah}{\hat{\bm{a}}} \newcommand{\ah}{\hat{a}} \newcommand{\vat}{\tilde{\bm{a}}} \newcommand{\at}{\tilde{a}}
+\newcommand{\vb}{\bm{b}} \newcommand{\vbh}{\hat{\bm{b}}} \newcommand{\bh}{\hat{b}} \newcommand{\vbt}{\tilde{\bm{b}}} \newcommand{\bt}{\tilde{b}}
+\newcommand{\vc}{\bm{c}} \newcommand{\vch}{\hat{\bm{c}}} \newcommand{\ch}{\hat{c}} \newcommand{\vct}{\tilde{\bm{c}}} \newcommand{\ct}{\tilde{c}}
+\newcommand{\vd}{\bm{d}} \newcommand{\vdh}{\hat{\bm{d}}} \newcommand{\dhat}{\hat{d}} \newcommand{\vdt}{\tilde{\bm{d}}} \newcommand{\dt}{\tilde{d}}
+\newcommand{\ve}{\bm{e}} \newcommand{\veh}{\hat{\bm{e}}} \newcommand{\eh}{\hat{e}} \newcommand{\vet}{\tilde{\bm{e}}} \newcommand{\et}{\tilde{e}}
+\newcommand{\vf}{\bm{f}} \newcommand{\vfh}{\hat{\bm{f}}} \newcommand{\fh}{\hat{f}} \newcommand{\vft}{\tilde{\bm{f}}} \newcommand{\ft}{\tilde{f}}
+\newcommand{\vg}{\bm{g}} \newcommand{\vgh}{\hat{\bm{g}}} \newcommand{\gh}{\hat{g}} \newcommand{\vgt}{\tilde{\bm{g}}} \newcommand{\gt}{\tilde{g}}
+\newcommand{\vh}{\bm{h}} \newcommand{\vhh}{\hat{\bm{h}}} \newcommand{\hh}{\hat{h}} \newcommand{\vht}{\tilde{\bm{h}}} \newcommand{\htild}{\tilde{h}}
+\newcommand{\vi}{\bm{i}} \newcommand{\vih}{\hat{\bm{i}}} \newcommand{\ih}{\hat{i}} \newcommand{\vit}{\tilde{\bm{i}}} \newcommand{\itild}{\tilde{i}}
+\newcommand{\vj}{\bm{j}} \newcommand{\vjh}{\hat{\bm{j}}} \newcommand{\jh}{\hat{j}} \newcommand{\vjt}{\tilde{\bm{j}}} \newcommand{\jt}{\tilde{j}}
+\newcommand{\vk}{\bm{k}} \newcommand{\vkh}{\hat{\bm{k}}} \newcommand{\kh}{\hat{k}} \newcommand{\vkt}{\tilde{\bm{k}}} \newcommand{\kt}{\tilde{k}}
+\newcommand{\vl}{\bm{l}} \newcommand{\vlh}{\hat{\bm{l}}} \newcommand{\lh}{\hat{l}} \newcommand{\vlt}{\tilde{\bm{l}}} \newcommand{\lt}{\tilde{l}}
+\newcommand{\vm}{\bm{m}} \newcommand{\vmh}{\hat{\bm{m}}} \newcommand{\mh}{\hat{m}} \newcommand{\vmt}{\tilde{\bm{m}}} \newcommand{\mt}{\tilde{m}}
+\newcommand{\vn}{\bm{n}} \newcommand{\vnh}{\hat{\bm{n}}} \newcommand{\nh}{\hat{n}} \newcommand{\vnt}{\tilde{\bm{n}}} \newcommand{\nt}{\tilde{n}}
+\newcommand{\vo}{\bm{o}} \newcommand{\voh}{\hat{\bm{o}}} \newcommand{\oh}{\hat{o}} \newcommand{\vot}{\tilde{\bm{o}}} \newcommand{\ot}{\tilde{o}}
+\newcommand{\vp}{\bm{p}} \newcommand{\vph}{\hat{\bm{p}}} \newcommand{\ph}{\hat{p}} \newcommand{\vpt}{\tilde{\bm{p}}} \newcommand{\pt}{\tilde{p}}
+\newcommand{\vq}{\bm{q}} \newcommand{\vqh}{\hat{\bm{q}}} \newcommand{\qh}{\hat{q}} \newcommand{\vqt}{\tilde{\bm{q}}} \newcommand{\qt}{\tilde{q}}
+\newcommand{\vr}{\bm{r}} \newcommand{\vrh}{\hat{\bm{r}}} \newcommand{\rh}{\hat{r}} \newcommand{\vrt}{\tilde{\bm{r}}} \newcommand{\rt}{\tilde{r}}
+\newcommand{\vs}{\bm{s}} \newcommand{\vsh}{\hat{\bm{s}}} \newcommand{\sh}{\hat{s}} \newcommand{\vst}{\tilde{\bm{s}}} \newcommand{\st}{\tilde{s}}
+\newcommand{\vt}{\bm{t}} \newcommand{\vth}{\hat{\bm{t}}} \newcommand{\that}{\hat{t}} \newcommand{\vtt}{\tilde{\bm{t}}} \newcommand{\ttil}{\tilde{t}}
+\newcommand{\vu}{\bm{u}} \newcommand{\vuh}{\hat{\bm{u}}} \newcommand{\uh}{\hat{u}} \newcommand{\vut}{\tilde{\bm{u}}} \newcommand{\ut}{\tilde{u}}
+\newcommand{\vv}{\bm{v}} \newcommand{\vvh}{\hat{\bm{v}}} \newcommand{\vhat}{\hat{v}} \newcommand{\vvt}{\tilde{\bm{v}}} \newcommand{\vtild}{\tilde{v}}
+\newcommand{\vw}{\bm{w}} \newcommand{\vwh}{\hat{\bm{w}}} \newcommand{\wh}{\hat{w}} \newcommand{\vwt}{\tilde{\bm{w}}} \newcommand{\wt}{\tilde{w}}
+\newcommand{\vx}{\bm{x}} \newcommand{\vxh}{\hat{\bm{x}}} \newcommand{\xh}{\hat{x}} \newcommand{\vxt}{\tilde{\bm{x}}} \newcommand{\xt}{\tilde{x}}
+\newcommand{\vy}{\bm{y}} \newcommand{\vyh}{\hat{\bm{y}}} \newcommand{\yh}{\hat{y}} \newcommand{\vyt}{\tilde{\bm{y}}} \newcommand{\yt}{\tilde{y}}
+\newcommand{\vz}{\bm{z}} \newcommand{\vzh}{\hat{\bm{z}}} \newcommand{\zh}{\hat{z}} \newcommand{\vzt}{\tilde{\bm{z}}} \newcommand{\zt}{\tilde{z}}
+
+\newcommand{\valpha}{\bm{\alpha}}
+\newcommand{\vbeta}{\bm{\beta}}
+\newcommand{\vgamma}{\bm{\gamma}}
+\newcommand{\vtheta}{\bm{\theta}}
+\newcommand{\vlambda}{\bm{\lambda}}
+\newcommand{\vmu}{\bm{\mu}}
+\newcommand{\vomega}{\bm{\omega}}
+
+\newcommand{\mSigma}{\bm{\Sigma}}
+
+\newcommand{\Fc}{\mathcal{F}}
+\newcommand{\Xc}{\mathcal{X}}
+\newcommand{\Yc}{\mathcal{Y}}
+\newcommand{\Zc}{\mathcal{Z}}
+\newcommand{\Gc}{\mathcal{G}}
+\newcommand{\Hc}{\mathcal{H}}
+\newcommand{\Dc}{\mathcal{D}}
+\newcommand{\Cc}{\mathcal{C}}
+\newcommand{\Rc}{\mathcal{R}}
+\newcommand{\Lc}{\mathcal{L}}
+\newcommand{\Nc}{\mathcal{N}}
+\newcommand{\Tc}{\mathcal{T}}
+
+% matrices
+\newcommand{\ma}{\bm{A}}
+\newcommand{\mb}{\bm{B}}
+\newcommand{\md}{\bm{D}}
+\newcommand{\mH}{\bm{H}}
+\newcommand{\mE}{\bm{E}}
+\newcommand{\mi}{\bm{I}}
+\newcommand{\mk}{\bm{K}}
+\newcommand{\ml}{\bm{L}}
+\newcommand{\mn}{\bm{N}}
+\newcommand{\mP}{\bm{P}}
+\newcommand{\mq}{\bm{Q}}
+\newcommand{\mr}{\bm{R}}
+\newcommand{\mU}{\bm{U}}
+\newcommand{\mv}{\bm{V}}
+\newcommand{\mw}{\bm{W}}
+\newcommand{\mx}{\bm{X}}
+\newcommand{\my}{\bm{Y}}
+\newcommand{\mz}{\bm{Z}}
+
+% tensors
+\newcommand{\tp}{\mathsf{P}}
+\newcommand{\tu}{\mathsf{U}}
+\newcommand{\tx}{\mathsf{X}}
+\newcommand{\ty}{\mathsf{Y}}
+\newcommand{\tz}{\mathsf{Z}}
+\newcommand{\tw}{\mathsf{W}}
+\newcommand{\tf}{\mathsf{F}}
+\newcommand{\ta}{\mathsf{A}}
+\renewcommand{\th}{\mathsf{H}}
+
+% norms
+\newcommand{\mynorm}[2]{\| {#1} \|_{#2}}
+\newcommand{\norm}[2]{\mynorm{#1}{#2}}
+\newcommand{\bignorm}[2]{\left\| {#1} \right\|_{#2}}
+\newcommand{\norml}[1]{\mynorm{#1}{1}}
+\newcommand{\bignorml}[1]{\bignorm{#1}{1}}
+\newcommand{\infnorm}[1]{\mynorm{#1}{\infty}}
+\newcommand{\biginfnorm}[1]{\bignorm{#1}{\infty}}
+\newcommand{\oneinf}{\ell_{1,\infty}}
+\newcommand{\onetwo}{\ell_{1,2}}
+\newcommand{\oneinfnorm}[1]{\mynorm{#1}{1,\infty}}
+\newcommand{\bigoneinf}[1]{\bignorm{#1}{1,\infty}}
+\newcommand{\onetwonorm}[1]{\mynorm{#1}{1,2}}
+\newcommand{\bigonetwo}[1]{\bignorm{#1}{1,2}}
+\newcommand{\enorm}[1]{\mynorm{#1}{2}}
+\newcommand{\bigenorm}[1]{\bignorm{#1}{2}}
+\newcommand{\znorm}[1]{\mynorm{#1}{0}}
+\newcommand{\bigznorm}[1]{\bignorm{#1}{0}}
+\newcommand{\frob}[1]{\|{#1}\|_{\text{F}}}
+\newcommand{\bigfrob}[1]{\bignorm{#1}{\text{F}}}
+\newcommand{\grpnorm}[2]{\norm{#1}{\text{Gr}(#2)}}
+
+% math operators
+\DeclareMathOperator*{\argmin}{argmin}
+\DeclareMathOperator*{\argmax}{argmax}
+\DeclareMathOperator{\divg}{div}
+\DeclareMathOperator{\dom}{dom}
+\DeclareMathOperator{\interior}{int}
+\DeclareMathOperator{\ri}{ri}
+\DeclareMathOperator{\sgn}{sgn}
+\DeclareMathOperator{\trace}{Tr}
+\DeclareMathOperator{\diag}{diag}
+\DeclareMathOperator{\rank}{rank}
+\DeclareMathOperator{\range}{range}
+\DeclareMathOperator{\vect}{vec}
+\DeclareMathOperator{\prox}{prox}
+\DeclareMathOperator{\intr}{int}
+\DeclareMathOperator{\relint}{ri}
+\DeclareMathOperator{\hard}{hard}
+\DeclareMathOperator{\id}{id}
+% \DeclareMathOperator{\tf}{tf}
+% \DeclareMathOperator{\idf}{idf}
+
+% misc
+\newcommand{\gs}{\geqslant}
+\newcommand{\ls}{\leqslant}
+\newcommand{\set}[1]{\left\{ {#1}\right\}}
+
+\newcommand{\defeq}{\ \stackrel{\text{def}}{=}\ }
+\newcommand{\ip}[2]{\left\langle#1, #2\right\rangle}
+\newcommand{\reals}{\mathbb{R}}
+\newcommand{\complex}{\mathbb{C}}
+\newcommand{\half}{\frac{1}{2}}