From: Michael Orlitzky <michael@orlitzky.com>
Date: Fri, 13 Mar 2020 00:05:58 +0000 (-0400)
Subject: mjo-linear_algebra.tex: add \diag{} to build diagonal matrices.
X-Git-Url: https://gitweb.michael.orlitzky.com/?a=commitdiff_plain;h=10b83af54da036b9f3122b5e82b18816c5acf386;p=mjotex.git

mjo-linear_algebra.tex: add \diag{} to build diagonal matrices.
---

diff --git a/examples.tex b/examples.tex
index 1d79079..c3e22e7 100644
--- a/examples.tex
+++ b/examples.tex
@@ -176,14 +176,16 @@
     matrices $A$ and $B$ is $\kp{A}{B}$. The adjoint of the operator
     $L$ is $\adjoint{L}$, or if it's a matrix, then its transpose is
     $\transpose{L}$. Its trace is $\trace{L}$, and its spectrum---the
-    set of its eigenvalues---is $\spectrum{L}$. Another matrix-specific
-    concept is the Moore-Penrose pseudoinverse of $L$, denoted by
-    $\pseudoinverse{L}$. Finally, the rank of a matrix $L$ is
-    $\rank{L}$. As far as matrix spaces go, we have the $n$-by-$n$
+    set of its eigenvalues---is $\spectrum{L}$. Another
+    matrix-specific concept is the Moore-Penrose pseudoinverse of $L$,
+    denoted by $\pseudoinverse{L}$. Finally, the rank of a matrix $L$
+    is $\rank{L}$. 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.
+    Cartesian product in this case. A handy way to represent the
+    matrix $A \in \Rn[n \times n]$ whose only non-zero entries are on
+    the diagonal is $\diag{\colvec{A_{11},A_{22},\ldots,A_{nn}}}$.
 
     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-linear_algebra.tex b/mjo-linear_algebra.tex
index d493b9c..c57e9b9 100644
--- a/mjo-linear_algebra.tex
+++ b/mjo-linear_algebra.tex
@@ -51,6 +51,11 @@
 % The trace of an operator.
 \newcommand*{\trace}[1]{ \operatorname{trace}\of{{#1}} }
 
+% The diagonal matrix whose only nonzero entries are on the diagonal
+% and are given by our argument. The argument should therefore be a
+% vector or tuple of entries, by convention going from the top-left to
+% the bottom-right of the matrix.
+\newcommand*{\diag}[1]{\operatorname{diag}\of{{#1}}}
 
 % The "rank" of its argument, which is context-dependent. It can mean
 % any or all of,