mjo-cone.tex: add the strictly positive orthant, \Rnplusplus.

[mjotex.git] / examples.tex

diff --git a/examples.tex b/examples.tex
index 015c5fd67df5aa3e5d4c272c60480694d20ba1ba..e70e0e1e0c63ad2d12ef667ebde7e69d9a6a0ad7 100644 (file)
--- a/examples.tex
+++ b/examples.tex
@@ -57,7 +57,7 @@
           \State{Rearrange $M$ randomly}
         \EndWhile{}
 
-        \Return{$M$}
+        \State{\Return{$M$}}
       \end{algorithmic}
     \end{algorithm}
   \end{section}
@@ -139,12 +139,12 @@
 
   \begin{section}{Cone}
     The dual cone of $K$ is $\dual{K}$. Some familiar symmetric cones
-    are $\Rnplus$, $\Lnplus$, $\Snplus$, and $\Hnplus$.  If cones
-    $K_{1}$ and $K_{2}$ are given, we can define $\posops{K_{1}}$,
-    $\posops[K_{2}]{K_{1}}$, $\Sof{K_{1}}$, $\Zof{K_{1}}$,
-    $\LL{K_{1}}$, and $\lyapunovrank{K_{1}}$. We can also define $x
-    \gecone_{K} y$, $x \gtcone_{K} y$, $x \lecone_{K} y$, and $x
-    \ltcone_{K} y$ with respect to a cone $K$.
+    are $\Rnplus$, $\Rnplusplus$, $\Lnplus$, $\Snplus$, and $\Hnplus$.
+    If cones $K_{1}$ and $K_{2}$ are given, we can define
+    $\posops{K_{1}}$, $\posops[K_{2}]{K_{1}}$, $\Sof{K_{1}}$,
+    $\Zof{K_{1}}$, $\LL{K_{1}}$, and $\lyapunovrank{K_{1}}$. We can
+    also define $x \gecone_{K} y$, $x \gtcone_{K} y$, $x \lecone_{K}
+    y$, and $x \ltcone_{K} y$ with respect to a cone $K$.
   \end{section}
 
   \begin{section}{Convex}
@@ -172,6 +172,11 @@
     \end{itemize}
   \end{section}
 
+  \begin{section}{Hurwitz}
+    Here lies the Hurwitz algebras, like the quaternions
+    $\quaternions$ and octonions $\octonions$.
+  \end{section}
+
   \begin{section}{Linear algebra}
     The absolute value of $x$ is $\abs{x}$, or its norm is
     $\norm{x}$. The inner product of $x$ and $y$ is $\ip{x}{y}$ and
@@ -203,7 +208,8 @@
     instead.
 
     If you want to solve a system of equations, try Cramer's
-    rule~\cite{ehrenborg}.
+    rule~\cite{ehrenborg}. Or at least the reduced row-echelon form of
+    the matrix, $\rref{A}$.
 
     The direct sum of $V$ and $W$ is $\directsum{V}{W}$, of course,
     but what if $W = V^{\perp}$? Then we wish to indicate that fact by