X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo-cone.tex;h=b770d753ec3ad8855a0ab91081550ee106737056;hb=d049732b73c04fe93839b552c403e731c0d5d8fc;hp=c556f4b14338306b8537a931f7f91c7588e5e310;hpb=9e823aa3dcf40f8bfd113476da576fb6b4c0180f;p=mjotex.git

diff --git a/mjo-cone.tex b/mjo-cone.tex
index c556f4b..b770d75 100644
--- a/mjo-cone.tex
+++ b/mjo-cone.tex
@@ -11,7 +11,7 @@
 
 % The dual of a subset of an inner-product space; always a closed
 % convex cone.
-\newcommand*{\dual}[1]{ {#1}^{*} }
+\newcommand*{\dual}[1]{ #1^{*} }
 
 %
 % Common cones.
@@ -59,25 +59,11 @@
 % The space of Lyapunov-like operators on its argument.
 \newcommand*{\LL}[1]{ \mathbf{LL}\of{ {#1} } }
 
+% The Lyapunov rank of the given cone.
+\newcommand*{\lyapunovrank}[1]{ \beta\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} }
-\newcommand*{\gtkstar}{ \ineqkstar{\gtk} }
-\newcommand*{\lekstar}{ \ineqkstar{\lek} }
-\newcommand*{\ltkstar}{ \ineqkstar{\ltk} }
-
-% And negated versions of some of those...
-\newcommand*{\ngeqkstar}{ \ineqkstar{\nsucceq} }
-\newcommand*{\ngtrkstar}{ \ineqkstar{\nsucc} }
+\newcommand*{\gecone}{\succcurlyeq}
+\newcommand*{\gtcone}{\succ}
+\newcommand*{\lecone}{\preccurlyeq}
+\newcommand*{\ltcone}{\prec}