X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo-linear_algebra.tex;h=204ad05bd6b7981d32e2c56a4b268642d58d4ce2;hb=6759e3a5bd5fd13bd239ee851c66d1eac83a7c1b;hp=02e1d12aba4d6383ee2b79f44eea272d96457329;hpb=910a2a081216b966d80e888d62cd3dcfae7418d5;p=mjotex.git

diff --git a/mjo-linear_algebra.tex b/mjo-linear_algebra.tex
index 02e1d12..204ad05 100644
--- a/mjo-linear_algebra.tex
+++ b/mjo-linear_algebra.tex
@@ -1,15 +1,22 @@
 %
 % Standard operations from linear algebra.
 %
+\ifx\havemjolinearalgebra\undefined
+\def\havemjolinearalgebra{1}
 
-% Needed for \lvert, \rVert, etc. and \operatorname.
-\usepackage{amsmath}
 
-% Wasysym contains the \ocircle that we use in \directsumperp.
-\usepackage{wasysym}
+\ifx\lvert\undefined
+  \usepackage{amsmath} % \lvert, \rVert, etc. and \operatorname.
+\fi
 
-% Part of the adjustbox package; needed to clip the \perp sign.
-\usepackage{trimclip}
+\ifx\ocircle\undefined
+  \usepackage{wasysym}
+\fi
+
+\ifx\clipbox\undefined
+  % Part of the adjustbox package; needed to clip the \perp sign.
+  \usepackage{trimclip}
+\fi
 
 \input{mjo-common}
 
@@ -37,9 +44,24 @@
 % 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}} }
 
+
+% The "rank" of its argument, which is context-dependent. It can mean
+% any or all of,
+%
+%   * the rank of a matrix,
+%   * the rank of a power-associative algebra (particularly an EJA),
+%   * the rank of an element in a Euclidean Jordan algebra.
+%
+\newcommand*{\rank}[1]{ \operatorname{rank}\of{{#1}} }
+
+
 % The ``span of'' operator. The name \span is already taken.
 \newcommand*{\spanof}[1]{ \operatorname{span}\of{{#1}} }
 
@@ -62,7 +84,7 @@
 \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
@@ -95,3 +117,6 @@
 
 % Now declare an orthogonal direct sum in terms of \oplusperp.
 \newcommand*{\directsumperp}[2]{ {#1}\oplusperp{#2} }
+
+
+\fi