From: Michael Orlitzky <michael@orlitzky.com>
Date: Mon, 4 Nov 2019 14:02:59 +0000 (-0500)
Subject: mjo-common: move \Sn and \Hn into mjo-linear_algebra.
X-Git-Url: https://gitweb.michael.orlitzky.com/?a=commitdiff_plain;h=fe30cc3cf8f9a88785d2899d00a727931377bb5d;p=mjotex.git

mjo-common: move \Sn and \Hn into mjo-linear_algebra.
---

diff --git a/examples.tex b/examples.tex
index a2e9cf3..0656165 100644
--- a/examples.tex
+++ b/examples.tex
@@ -117,11 +117,7 @@
     superscript when that superscript would be one: $\Nn[1]$,
     $\Zn[1]$, $\Qn[1]$, $\Rn[1]$, $\Cn[1]$. However, if the
     superscript is (say) two, then it appears: $\Nn[2]$, $\Zn[2]$,
-    $\Qn[2]$, $\Rn[2]$, $\Cn[2]$. Likewise we have the $n$-by-$n$
-    real-symmetric and complex-Hermitian matrices $\Sn$ and $\Hn$
-    respectively; however $\Sn[1]$ and $\Hn[1]$ do not automatically
-    simplify because the ``$n$'' does not indicate the arity of a
-    Cartesian product in this case.
+    $\Qn[2]$, $\Rn[2]$, $\Cn[2]$.
 
     We also have a few basic set operations, for example the union of
     two or three sets: $\union{A}{B}$, $\unionthree{A}{B}{C}$. And of
@@ -196,7 +192,11 @@
     $\transpose{L}$. Its trace is $\trace{L}$. Another matrix-specific
     concept is the Moore-Penrose pseudoinverse of $L$, denoted by
     $\pseudoinverse{L}$. Finally, the rank of a matrix $L$ is
-    $\rank{L}$.
+    $\rank{L}$. As far as matrix spaces go, we have the $n$-by-$n$
+    real-symmetric and complex-Hermitian matrices $\Sn$ and $\Hn$
+    respectively; however $\Sn[1]$ and $\Hn[1]$ do not automatically
+    simplify because the ``$n$'' does not indicate the arity of a
+    Cartesian product in this case.
 
     The span of a set $X$ is $\spanof{X}$, and its codimension is
     $\codim{X}$. The projection of $X$ onto $V$ is $\proj{V}{X}$. The
diff --git a/mjo-common.tex b/mjo-common.tex
index 5971547..2819bdc 100644
--- a/mjo-common.tex
+++ b/mjo-common.tex
@@ -138,31 +138,6 @@
 \fi
 
 
-% The space of real symmetric n-by-n matrices. Does not reduce to
-% merely "S" when n=1 since S^{n} does not mean an n-fold cartesian
-% product of S^{1}.
-\newcommand*{\Sn}[1][n]{ \mathcal{S}^{#1} }
-\ifdefined\newglossaryentry
-  \newglossaryentry{Sn}{
-    name={\ensuremath{\Sn}},
-    description={the set of $n$-by-$n$ real symmetric matrices},
-    sort=Sn
-  }
-\fi
-
-% The space of complex Hermitian n-by-n matrices. Does not reduce to
-% merely "H" when n=1 since H^{n} does not mean an n-fold cartesian
-% product of H^{1}.
-\newcommand*{\Hn}[1][n]{ \mathcal{H}^{#1} }
-\ifdefined\newglossaryentry
-  \newglossaryentry{Hn}{
-    name={\ensuremath{\Hn}},
-    description={the set of $n$-by-$n$ complex Hermitian matrices},
-    sort=Hn
-  }
-\fi
-
-
 %
 % Basic set operations
 %
diff --git a/mjo-linear_algebra.tex b/mjo-linear_algebra.tex
index 204ad05..267ef67 100644
--- a/mjo-linear_algebra.tex
+++ b/mjo-linear_algebra.tex
@@ -119,4 +119,29 @@
 \newcommand*{\directsumperp}[2]{ {#1}\oplusperp{#2} }
 
 
+% The space of real symmetric n-by-n matrices. Does not reduce to
+% merely "S" when n=1 since S^{n} does not mean an n-fold cartesian
+% product of S^{1}.
+\newcommand*{\Sn}[1][n]{ \mathcal{S}^{#1} }
+\ifdefined\newglossaryentry
+  \newglossaryentry{Sn}{
+    name={\ensuremath{\Sn}},
+    description={the set of $n$-by-$n$ real symmetric matrices},
+    sort=Sn
+  }
+\fi
+
+% The space of complex Hermitian n-by-n matrices. Does not reduce to
+% merely "H" when n=1 since H^{n} does not mean an n-fold cartesian
+% product of H^{1}.
+\newcommand*{\Hn}[1][n]{ \mathcal{H}^{#1} }
+\ifdefined\newglossaryentry
+  \newglossaryentry{Hn}{
+    name={\ensuremath{\Hn}},
+    description={the set of $n$-by-$n$ complex Hermitian matrices},
+    sort=Hn
+  }
+\fi
+
+
 \fi