mjo-linear_algebra: add the \spectrum{} of a linear operator.

diff --git a/examples.tex b/examples.tex
index c7959732d44ce74297d43c228dd90ae267dd255a..0cf8afa51a90a84b624fee9a7f4232ae7ff9a52d 100644 (file)
--- a/examples.tex
+++ b/examples.tex
@@ -170,7 +170,8 @@
     their tensor product is $\tp{x}{y}$. The Kronecker product of
     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 $\trace{L}$. Another matrix-specific
+    $\transpose{L}$. 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-$n$

diff --git a/mjo-linear_algebra.tex b/mjo-linear_algebra.tex
index c1aa9f57650112330673f93985d6e1cd655c2594..d493b9cce5bd047eeb940a972128a6cf7198d261 100644 (file)
--- a/mjo-linear_algebra.tex
+++ b/mjo-linear_algebra.tex
@@ -71,6 +71,19 @@
 % The orthogonal projection of its second argument onto the first.
 \newcommand*{\proj}[2] { \operatorname{proj}\of{#1, #2} }
 
+% The set of all eigenvalues of its argument, which should be either a
+% matrix or a linear operator. The sigma notation was chosen instead
+% of lambda so that lambda can be reserved to denote the ordered tuple
+% (largest to smallest) of eigenvalues.
+\newcommand*{\spectrum}[1]{\sigma\of{{#1}}}
+\ifdefined\newglossaryentry
+  \newglossaryentry{spectrum}{
+    name={\ensuremath{\spectrum{L}}},
+    description={the set of all eigenvalues of $L$},
+    sort=s
+  }
+\fi
+
 % The ``Automorphism group of'' operator.
 \newcommand*{\Aut}[1]{ \operatorname{Aut}\of{{#1}} }