low-rank-hadamard/basicincludes.tex at master · rustandruin/low-rank-hadamard · GitHub

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
\usepackage{graphicx}
\usepackage{amssymb,bm}
\usepackage{setspace}
\usepackage{multirow}
\usepackage{colonequals}
\usepackage{enumerate}

\evensidemargin=0in
\oddsidemargin=0in
\textwidth=6.5in
\topmargin=-0.33in
\headheight=0.25in
\textheight=9in

\renewcommand{\star}{*}

%\newcommand{\mat}[1]{\ensuremath{\bm{#1}}}
\renewcommand{\vec}[1]{\ensuremath{\bm{#1}}}
%\newcommand{\e}{\ensuremath{\mathrm{e}}}
%\newcommand{\E}{\ensuremath{\mathbb{E}}}
%\newcommand{\Prob}[1]{\ensuremath{\mathbb{P}\left(#1\right)}}
\newcommand{\CondProb}[2]{\ensuremath{\mathbb{P}\left\{#1 \,\left|\, #2 \right.\right\}}}
\newcommand{\lnorm}[2]{\ensuremath{\left\| #2 \right\|_{L_{#1}}}}
%\newcommand{\R}{\ensuremath{\mathbb{R}}}
%\newcommand{\C}{\ensuremath{\mathbb{C}}}
\newcommand{\Z}{\ensuremath{\mathbb{Z}}}
\newcommand{\N}{\ensuremath{\mathbb{N}}}
\newcommand{\randcon}{\ensuremath{\mathrm{R}}}
\newcommand{\indicator}[1]{\ensuremath{\mathbb{1}\left\{#1\right\}}}
\newcommand{\const}[1]{\ensuremath{\mathrm{#1}}}

%\newcommand{\norm}[1]{\ensuremath{\big\|#1\big\|}}
\newcommand{\F}{F}

\newcommand{\lambdamin}[1]{\ensuremath{\lambda_{\mathrm{min}}\left(#1\right)}}
\newcommand{\sigmamin}[1]{\ensuremath{\sigma_{\mathrm{min}}\left(#1\right)}}
\newcommand{\Isom}[2]{\ensuremath{V_{#1}(\C^{#2})}}
\DeclareMathOperator{\tr}{tr}
%\DeclareMathOperator{\rank}{rank}
\newcommand{\trexp}[1]{\ensuremath{\tr\exp\left(#1\right)}}
%\newcommand{\diag}[1]{\ensuremath{\operatorname{diag}\left(#1\right)}}

%\newtheorem{thm}{Theorem}
\newtheorem{prop}{Proposition}
%\newtheorem{lemma}{Lemma}
\newtheorem{cor}{Corollary}
\newtheorem{defn}{Definition}
\theoremstyle{remark}
\newtheorem{remark}{Remark}