r21643 - /branches/relax_disp/docs/latex/dispersion.tex -- November 25, 2013 - 14:11

Author: bugman
Date: Mon Nov 25 14:11:48 2013
New Revision: 21643

URL: http://svn.gna.org/viewcvs/relax?rev=21643&view=rev
Log:
Updates for the 'MMQ 2-site' model equations in the manual.


Modified:
    branches/relax_disp/docs/latex/dispersion.tex

Modified: branches/relax_disp/docs/latex/dispersion.tex
URL: 
http://svn.gna.org/viewcvs/relax/branches/relax_disp/docs/latex/dispersion.tex?rev=21643&r1=21642&r2=21643&view=diff
==============================================================================
--- branches/relax_disp/docs/latex/dispersion.tex (original)
+++ branches/relax_disp/docs/latex/dispersion.tex Mon Nov 25 14:11:48 2013
@@ -871,17 +871,27 @@
     \mathbf{A} &= \left( \mathbf{M_1} \mathbf{M_2} \mathbf{M_2} \mathbf{M_1} 
\right)^{\frac{n}{2}}, \\
     \mathbf{B} &= \left( \mathbf{M_2}^* \mathbf{M_1}^* \mathbf{M_1}^* 
\mathbf{M_2}^* \right)^{\frac{n}{2}}, \\
     \mathbf{C} &= \left( \mathbf{M_2} \mathbf{M_1} \mathbf{M_1} \mathbf{M_2} 
\right)^{\frac{n}{2}}, \\
-    \mathbf{D} &= \left( \mathbf{M_1}^* \mathbf{M_2}^* \mathbf{M_2}^* 
\mathbf{M_1}^* \right)^{\frac{n}{2}},
+    \mathbf{D} &= \left( \mathbf{M_1}^* \mathbf{M_2}^* \mathbf{M_2}^* 
\mathbf{M_1}^* \right)^{\frac{n}{2}}.
 \end{align}
 \end{subequations}
 
-and when $n$ is odd, they are defined as
+When $n$ is odd, they are defined as
 \begin{subequations}
 \begin{align}
     \mathbf{A} &= \left( \mathbf{M_1} \mathbf{M_2} \mathbf{M_2} \mathbf{M_1} 
\right)^{\frac{n-1}{2}} \mathbf{M_1} \mathbf{M_2}, \\
     \mathbf{B} &= \left( \mathbf{M_1}^* \mathbf{M_2}^* \mathbf{M_2}^* 
\mathbf{M_1}^* \right)^{\frac{n-1}{2}} \mathbf{M_1}^* \mathbf{M_2}^*, \\
     \mathbf{C} &= \left( \mathbf{M_2} \mathbf{M_1} \mathbf{M_1} \mathbf{M_2} 
\right)^{\frac{n-1}{2}} \mathbf{M_2} \mathbf{M_1}, \\
     \mathbf{D} &= \left( \mathbf{M_2}^* \mathbf{M_1}^* \mathbf{M_1}^* 
\mathbf{M_2}^* \right)^{\frac{n-1}{2}} \mathbf{M_2}^* \mathbf{M_1}^*.
+\end{align}
+\end{subequations}
+
+When $n$ is zero, to avoid matrix powers of zero they are defined as
+\begin{subequations}
+\begin{align}
+    \mathbf{A} &= \mathbf{M_1} \mathbf{M_2}, \\
+    \mathbf{B} &= \mathbf{M_1}^* \mathbf{M_2}^*, \\
+    \mathbf{C} &= \mathbf{M_2} \mathbf{M_1}, \\
+    \mathbf{D} &= \mathbf{M_2}^* \mathbf{M_1}^*.
 \end{align}
 \end{subequations}