Fix a typo and reorder the \trace command.

[mjotex.git] / mjo-linear_algebra.tex

diff --git a/mjo-linear_algebra.tex b/mjo-linear_algebra.tex
index 380c3bf546317349b20adedd1974bb82da6ed9f6..ebf4acddc359c7b02b6c9f81f29b05564a6290d8 100644 (file)
--- a/mjo-linear_algebra.tex
+++ b/mjo-linear_algebra.tex
@@ -7,14 +7,14 @@
 
 \input{mjo-common}
 
-% Absolute value (modulis) of a scalar.
+% Absolute value (modulus) 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.
-\newcommand*{\ip}[2]{\langle{#1},{#2}\rangle}
+\newcommand*{\ip}[2]{\left\langle{#1},{#2}\right\rangle}
 
 % The tensor product of its two arguments.
 \newcommand*{\tp}[2]{ {#1}\otimes{#2} }
@@ -27,15 +27,19 @@
 % The adjoint of a linear operator.
 \newcommand*{\adjoint}[1]{ #1^{*} }
 
+% The ``transpose'' of a linear operator; namely, the adjoint, but
+% specialized to real matrices.
+\newcommand*{\transpose}[1]{ #1^{T} }
+
+% The trace of an operator.
+\newcommand*{\trace}[1]{ \operatorname{trace}\of{{#1}} }
+
 % The ``span of'' operator. The name \span is already taken.
 \newcommand*{\spanof}[1]{ \operatorname{span}\of{{#1}} }
 
 % The ``co-dimension of'' operator.
 \newcommand*{\codim}{ \operatorname{codim} }
 
-% The trace of an operator.
-\newcommand*{\trace}[1]{ \operatorname{trace}\of{{#1}} }
-
 % The orthogonal projection of its second argument onto the first.
 \newcommand*{\proj}[2] { \operatorname{proj}\of{#1, #2} }