From: Michael Orlitzky <michael@orlitzky.com>
Date: Mon, 25 Apr 2016 14:18:26 +0000 (-0400)
Subject: Add some common cones to mjo-cone.
X-Git-Tag: posZ-submitted-laa~46
X-Git-Url: http://gitweb.michael.orlitzky.com/?p=mjotex.git;a=commitdiff_plain;h=ad5dafa4ee98c4729b33bebc1817c09cae1b881a

Add some common cones to mjo-cone.
---

diff --git a/mjo-cone.tex b/mjo-cone.tex
index 16d1654..1199d4f 100644
--- a/mjo-cone.tex
+++ b/mjo-cone.tex
@@ -9,6 +9,27 @@
 
 \input{mjo-common}
 
+%
+% Common cones.
+%
+
+% The nonnegative orthant in the given number of dimensions.
+\newcommand*{\Rnplus}[1][n]{ \mathbb{R}^{{#1}}_{+} }
+
+% The Lorentz ``ice-cream'' cone in the given number of dimensions.
+\newcommand*{\Lnplus}[1][n]{ \mathcal{L}^{{#1}}_{+} }
+
+% The PSD cone in a space of symmetric matrices.
+\newcommand*{\Snplus}[1][n]{ \mathcal{S}^{{#1}}_{+} }
+
+% The PSD cone in a space of Hermitian matrices.
+\newcommand*{\Hnplus}[1][n]{ \mathcal{H}^{{#1}}_{+} }
+
+
+%
+% Some collections of linear operators
+%
+
 % The set of all S-operators on its argument.
 \newcommand*{\Sof}[1]{ \mathbf{S} \of{ {#1} } }
 
@@ -18,12 +39,18 @@
 % The space of Lyapunov-like operators on its argument.
 \newcommand*{\LL}[1]{ \mathbf{LL}\of{ {#1} } }
 
+
+%
 % Cone inequality operators.
+%
+
+% Standard cone inequalities.
 \newcommand*{\gek}{ \succcurlyeq }
 \newcommand*{\gtk}{ \succ }
 \newcommand*{\lek}{ \preccurlyeq }
 \newcommand*{\ltk}{ \prec }
 
+
 % Starred versions of the cone inequality operators.
 \newcommand*{\ineqkstar}[1]{ \mathrel{ \overset{ _{\ast} }{ #1 } } }
 \newcommand*{\gekstar}{ \ineqkstar{\gek} }