X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo-linear_algebra.tex;h=9e32d2179a25e1d061eeeb1f063ed14bcdf36284;hb=87aa4249a1cb51b6393e7d6f74276f00efc15df0;hp=0fce684a88ba6f8cac3e2136dca6d77c05ae198c;hpb=d6a9f13f45fead88404ee02cb446db2f3047eee8;p=mjotex.git

diff --git a/mjo-linear_algebra.tex b/mjo-linear_algebra.tex
index 0fce684..9e32d21 100644
--- a/mjo-linear_algebra.tex
+++ b/mjo-linear_algebra.tex
@@ -2,10 +2,19 @@
 % Standard operations from linear algebra.
 %
 
+% Needed for \lvert, \rVert, etc. and \operatorname.
+\usepackage{amsmath}
+
 \input{mjo-common}
 
+% Absolute value (modulis) of a scalar.
+\newcommand*{\abs}[1]{ \left\lvert {#1} \right\rvert }
+
+% Norm of a vector.
+\newcommand*{\norm}[1]{ \left\lVert {#1} \right\rVert }
+
 % The inner product between its two arguments.
-\DeclarePairedDelimiterX{\ip}[2]{ \langle }{ \rangle}{ {#1}, {#2} }
+\newcommand*{\ip}[2]{ \langle {#1}, {#2} \rangle }
 
 % The tensor product of its two arguments.
 \newcommand*{\tp}[2]{ {#1} \otimes {#2} }
@@ -34,5 +43,19 @@
 % The ``write a big vector as a matrix'' operator.
 \newcommand*{\matricize}[1]{ \operatorname{mat} \of{{#1}} }
 
-% The inverse of the adjoint of an operator (the argument).
-\newcommand*{\adjinv}[1]{ \left( {#1}^{*} \right)^{-1} }
+% An inline column vector, with parentheses and a transpose operator.
+\newcommand*{\colvec}[1]{ \left( {#1} \right)^{T} }
+
+% Bounded linear operators on some space. The required argument is the
+% domain of those operators, and the optional argument is the
+% codomain. If the optional argument is omitted, the required argument
+% is used for both.
+\newcommand*{\boundedops}[2][]{
+  \mathcal{B}\of{ {#2}
+    \if\relax\detokenize{#1}\relax
+      {}%
+    \else
+      {,{#1}}%
+    \fi
+  }
+}