X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo-linear_algebra.tex;h=d423a433e65030774141eac013cf95bbea2a1aa4;hb=ba0227140d34fe1c8cacdb4996b5896aec4c4013;hp=048022935b681bfe5f0d0c04366f7fadcb6383d2;hpb=5c4f67545f0988d065f1d52f90eed9233562c9fc;p=mjotex.git

diff --git a/mjo-linear_algebra.tex b/mjo-linear_algebra.tex
index 0480229..d423a43 100644
--- a/mjo-linear_algebra.tex
+++ b/mjo-linear_algebra.tex
@@ -1,6 +1,9 @@
 %
 % Standard operations from linear algebra.
 %
+\ifx\havemjolinearalgebra\undefined
+\def\havemjolinearalgebra{1}
+
 
 % Needed for \lvert, \rVert, etc. and \operatorname.
 \usepackage{amsmath}
@@ -37,6 +40,10 @@
 % specialized to real matrices.
 \newcommand*{\transpose}[1]{ #1^{T} }
 
+% The Moore-Penrose (or any other, I guess) pseudo-inverse of its
+% sole argument.
+\newcommand*{\pseudoinverse}[1]{ #1^{+} }
+
 % The trace of an operator.
 \newcommand*{\trace}[1]{ \operatorname{trace}\of{{#1}} }
 
@@ -62,7 +69,7 @@
 \newcommand*{\matricize}[1]{ \operatorname{mat}\of{{#1}} }
 
 % An inline column vector, with parentheses and a transpose operator.
-\newcommand*{\colvec}[1]{ \left({#1}\right)^{T} }
+\newcommand*{\colvec}[1]{ \transpose{\left({#1}\right)} }
 
 % Bounded linear operators on some space. The required argument is the
 % domain of those operators, and the optional argument is the
@@ -89,9 +96,12 @@
 \DeclareMathOperator{\oplusperp}{\mathbin{
   \ooalign{
     $\ocircle$\cr
-    \raisebox{0.65\height}{$\clipbox{0pt 0pt 0pt 0.5\height}{$\perp$}$}\cr
+    \raisebox{0.625\height}{$\clipbox{0pt 0pt 0pt 0.5\height}{$\perp$}$}\cr
   }
 }}
 
 % Now declare an orthogonal direct sum in terms of \oplusperp.
 \newcommand*{\directsumperp}[2]{ {#1}\oplusperp{#2} }
+
+
+\fi