mjo-algebra.tex: fix glossary sorting of \variety

[mjotex.git] / mjo-linear_algebra.tex

diff --git a/mjo-linear_algebra.tex b/mjo-linear_algebra.tex
index 267ef67ae96af8482d502fbd9751b7471122d878..5f2554484b2b1c28adea2cfb8e594eb01fa8970d 100644 (file)
--- a/mjo-linear_algebra.tex
+++ b/mjo-linear_algebra.tex
@@ -18,7 +18,7 @@
   \usepackage{trimclip}
 \fi
 
   \usepackage{trimclip}
 \fi
 

-\input{mjo-common}
+\input{mjo-common} % for \of, at least

 
 % Absolute value (modulus) of a scalar.
 \newcommand*{\abs}[1]{\left\lvert{#1}\right\rvert}
 
 % Absolute value (modulus) of a scalar.
 \newcommand*{\abs}[1]{\left\lvert{#1}\right\rvert}


@@ -51,6 +51,11 @@
 % The trace of an operator.
 \newcommand*{\trace}[1]{ \operatorname{trace}\of{{#1}} }
 
 % 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,
 
 % The "rank" of its argument, which is context-dependent. It can mean
 % any or all of,


@@ -71,6 +76,29 @@
 % The orthogonal projection of its second argument onto the first.
 \newcommand*{\proj}[2] { \operatorname{proj}\of{#1, #2} }
 
 % 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 reduced row-echelon form of its argument, a matrix.
+\newcommand*{\rref}[1]{\operatorname{rref}\of{#1}}
+\ifdefined\newglossaryentry
+  \newglossaryentry{rref}{
+    name={\ensuremath{\rref{A}}},
+    description={the reduced row-echelon form of $A$},
+    sort=r
+  }
+\fi
+

 % The ``Automorphism group of'' operator.
 \newcommand*{\Aut}[1]{ \operatorname{Aut}\of{{#1}} }
 
 % The ``Automorphism group of'' operator.
 \newcommand*{\Aut}[1]{ \operatorname{Aut}\of{{#1}} }
 


@@ -133,7 +161,9 @@
 
 % 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
 
 % 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}.
+% product of H^{1}. The field may also be given rather than assumed
+% to be complex; for example \Hn[3]\of{\mathbb{O}} might denote the
+% 3-by-3 Hermitian matrices with octonion entries.

 \newcommand*{\Hn}[1][n]{ \mathcal{H}^{#1} }
 \ifdefined\newglossaryentry
   \newglossaryentry{Hn}{
 \newcommand*{\Hn}[1][n]{ \mathcal{H}^{#1} }
 \ifdefined\newglossaryentry
   \newglossaryentry{Hn}{


@@ -144,4 +174,8 @@
 \fi
 
 
 \fi
 
 

+% The general linear group of square matrices whose size is the first
+% argument and whose entries come from the second argument.
+\newcommand*{\GL}[2]{\operatorname{GL}_{#1}\of{#2}}
+

 \fi
 \fi