X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo-cone.tex;h=a7507d60778bf4a01b560cb1b41c97e36a77ff9b;hb=98ccfbccb274901a2504e559f0e88372d11d5a3c;hp=16d16546f3f0294e9a50febd00a07d4ab936b4c7;hpb=b5df7cd8456ef72fd2e61a2bb0c47b89b0ffa07e;p=mjotex.git

diff --git a/mjo-cone.tex b/mjo-cone.tex
index 16d1654..a7507d6 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]{ \Rn[#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} } }
 
@@ -18,11 +39,17 @@
 % The space of Lyapunov-like operators on its argument.
 \newcommand*{\LL}[1]{ \mathbf{LL}\of{ {#1} } }
 
+
+%
 % Cone inequality operators.
-\newcommand*{\gek}{ \succcurlyeq }
-\newcommand*{\gtk}{ \succ }
-\newcommand*{\lek}{ \preccurlyeq }
-\newcommand*{\ltk}{ \prec }
+%
+
+% 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 } } }