# LaTeX2HTML 99.1 release (March 30, 1999)
# Associate images original text with physical files.


$key = q/{displaymath}widetilde{mathcal{M}}=left(array{{cc}1<col_mark>0<row_mark>u<col_mark>mathcal{M}<row_mark>array{right){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="140" HEIGHT="64" BORDER="0"
 SRC="img6.gif"
 ALT="\begin{displaymath}\widetilde{\mathcal{M}} =
\left(
\begin{array}{cc}
1 &amp; 0 \\\\
u &amp; \mathcal{M}\\\\
\end{array}
\right)\end{displaymath}">|; 

$key = q/,cinmathbb{R};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="img8.gif"
 ALT="$ \,c\in \mathbb {R}$">|; 

$key = q/,detwidetilde{mathcal{M}}=detmathcal{M}=pm1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="178" HEIGHT="46" ALIGN="MIDDLE" BORDER="0"
 SRC="img9.gif"
 ALT="$ \,det
\widetilde{\mathcal{M}} = det \mathcal{M} = \pm 1$">|; 

$key = q/;b=sqrt{-displaystylefrac{{detmathcal{A}}}{{lambda_1lambda_2}}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="121" HEIGHT="67" ALIGN="MIDDLE" BORDER="0"
 SRC="img22.gif"
 ALT="$ \;b = \sqrt{-\displaystyle\frac{{det
\mathcal{A}}}{{\lambda_1 \lambda_2}}}$">|; 

$key = q/,mathcal{M}inO(3),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="img1.gif"
 ALT="$ \,\mathcal{M} \in O(3) \,$">|; 

$key = q/,u;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="img5.gif"
 ALT="$ \,u$">|; 

$key = q/displaystylelambda_1x^2+lambda_2y^2+lambda_3z^2+frac{detmathcal{A}}{detmathcal{A}_0}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="268" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="img14.gif"
 ALT="$\displaystyle \lambda_1 x^2 + \lambda_2 y^2 + \lambda_3 z^2 + \frac{det
\mathcal{A}}{det \mathcal{A}_0} = 0
$">|; 

$key = q/displaystyledetmathcal{A}=detmathcal{B}=-b^2lambda_1lambda_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="201" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="img21.gif"
 ALT="$\displaystyle det \mathcal{A} = det \mathcal{B} = -b^2 \lambda_1 \lambda_2
$">|; 

$key = q/{displaymath}mathcal{B}:=left(array{{cccc}0<col_mark>0<col_mark>0<col_mark>b<rowrk>0<col_mark>0<col_mark>0<row_mark>array{right){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="190" HEIGHT="118" BORDER="0"
 SRC="img19.gif"
 ALT="\begin{displaymath}
\mathcal{B}\: = \left(
\begin{array}{cccc}
0 &amp; 0 &amp; 0 &amp; b ...
... \lambda_2 &amp; 0 \\\\
b &amp; 0 &amp; 0 &amp; 0 \\\\
\end{array}
\right)
\end{displaymath}">|; 

$key = q/,cneq0,lambda_1neq0,lambda_2neq0,lambda_3neq0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="240" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="img11.gif"
 ALT="$ \,c \neq 0, \lambda_1
\neq 0, \lambda_2 \neq 0, \lambda_3 \neq 0,$">|; 

$key = q/,b>0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="img20.gif"
 ALT="$ \,b &gt; 0\,$">|; 

$key = q/,mathcal{A}_0=2,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="img17.gif"
 ALT="$ \,\mathcal{A}_0 =2 \,$">|; 

$key = q/,lambda_3,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="img18.gif"
 ALT="$ \,\lambda_3 \,$">|; 

$key = q/;b=sqrt{displaystylefrac{{detmathcal{A}}}{{beta}}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="img26.gif"
 ALT="$ \;b =
\sqrt{\displaystyle\frac{{det \mathcal{A}}}{{\beta}}}$">|; 

$key = q/,mathcal{A}_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="img4.gif"
 ALT="$ \,\mathcal{A}_0 $">|; 

$key = q/,c=displaystylefrac{detmathcal{A}}{detmathcal{A}_0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="img13.gif"
 ALT="$ \,c=\displaystyle
\frac{det \mathcal{A}}{det \mathcal{A}_0}$">|; 

$key = q/,c;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="img12.gif"
 ALT="$ \,c$">|; 

$key = q/:mathcal{B}_0=,^tmathcal{M}mathcal{A}_0mathcal{M}:;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="136" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="img2.gif"
 ALT="$ \:\mathcal{B}_0 =
\,^t\mathcal{M} \mathcal{A}_0 \mathcal{M} \:$">|; 

$key = q/,beta,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="img25.gif"
 ALT="$ \,\beta \,$">|; 

$key = q/displaystylecdetmathcal{A}_0=clambda_1lambda_2lambda_3=detmathcal{B}=(detmathcal{Q})^2detmathcal{A}=detmathcal{A}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="412" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="img10.gif"
 ALT="$\displaystyle c det \mathcal{A}_0 = c \lambda_1 \lambda_2 \lambda_3 = det
\mathcal{B} = (det \mathcal{Q})^2 det \mathcal{A} = det
\mathcal{A}.
$">|; 

$key = q/{displaymath}mathcal{B}:=hspace{2mm}^twidetilde{mathcal{M}}hspace{1mm}mathcal{A}l_mark>0<col_mark>lambda_3<row_mark>array{right){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="313" HEIGHT="118" BORDER="0"
 SRC="img7.gif"
 ALT="\begin{displaymath}
\mathcal{B}\: = \hspace{2mm} ^t\widetilde{\mathcal{M}}
\hs...
..._2 &amp; 0 \\\\
0 &amp; 0 &amp; 0 &amp; \lambda_3 \\\\
\end{array}
\right)
\end{displaymath}">|; 

$key = q/;-displaystylefrac{{detmathcal{A}_0}}{{detmathcal{A}}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="img15.gif"
 ALT="$ \;-\displaystyle\frac{{det
\mathcal{A}_0}}{{det \mathcal{A}}}$">|; 

$key = q/,mathcal{A}_0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="img23.gif"
 ALT="$ \,\mathcal{A}_0 \,$">|; 

$key = q/,mathcal{Q},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="img16.gif"
 ALT="$ \,\mathcal{Q} \,$">|; 

$key = q/,mathcal{B}_0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="img3.gif"
 ALT="$ \,\mathcal{B}_0 \,$">|; 

$key = q/,lambda_1lambda_2,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="img24.gif"
 ALT="$ \,\lambda_1 \lambda_2 \,$">|; 

1;

