# LaTeX2HTML 99.1 release (March 30, 1999)
# Associate images original text with physical files.


$key = q/displaystyleP_{mathcal{A}_0}(lambda)=(2-lambda)((1-lambda)^2-1)=(2-lambda)^2lambda.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="364" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="img8.gif"
 ALT="$\displaystyle P_{\mathcal{A}_0}(\lambda)=(2-\lambda)((1-\lambda)^2-1)=(2-\lambda)^2\lambda.
$">|; 

$key = q/{displaymath}mathcal{A}:=left(array{{cccc}1<col_mark>0<col_mark>-2<col_mark>3slak>0<col_mark>-1<col_mark>1<row_mark>array{right){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="457" HEIGHT="118" BORDER="0"
 SRC="img2.gif"
 ALT="\begin{displaymath}
\mathcal{A}\: = \left(
\begin{array}{cccc}
1 &amp; 0 &amp; -2 &amp; 3...
... \\\\
0 &amp; 1 &amp; -1 \\\\
0 &amp; -1 &amp; 1 \\\\
\end{array}
\right)
\end{displaymath}">|; 

$key = q/;detmathcal{A}_0=0;;;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="img4.gif"
 ALT="$ \;det\mathcal{A}_0=0;\;$">|; 

$key = q/;r(mathcal{A}_0)=2.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="img5.gif"
 ALT="$ \;
r(\mathcal{A}_0)=2. $">|; 

$key = q/displaystylelambda_1x^2+lambda_2y^2-2bz=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="185" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="img12.gif"
 ALT="$\displaystyle \lambda_1x^2+\lambda_2y^2-2bz=0$">|; 

$key = q/;detmathcal{A}<0;;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="img6.gif"
 ALT="$ \;det\mathcal{A}&lt;0 \; $">|; 

$key = q/displaystyleqquadb=sqrt{-frac{detmathcal{A}}{lambda_1lambda_2}}=sqrt{frac{1}{8}}=frac{1}{2sqrt{2}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="279" HEIGHT="71" ALIGN="MIDDLE" BORDER="0"
 SRC="img13.gif"
 ALT="$\displaystyle \qquad
b=\sqrt{-\frac{det\mathcal{A}}{\lambda_1\lambda_2}}
=\sqrt{\frac{1}{8}}=\frac{1}{2\sqrt{2}}.
$">|; 

$key = q/;detmathcal{A}=-frac{displaystyle1}{displaystyle2};Rightarrow;r(mathcal{A})=4;;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="222" HEIGHT="48" ALIGN="MIDDLE" BORDER="0"
 SRC="img3.gif"
 ALT="$ \;det\mathcal{A}=-\frac{\displaystyle 1}{\displaystyle
2} \; \Rightarrow \; r(\mathcal{A})=4\; $">|; 

$key = q/:mathcal{A}_0:;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="img7.gif"
 ALT="$ \:\mathcal{A}_0 \:$">|; 

$key = q/;lambda_1=2,;lambda_2=2,;lambda_3=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="201" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="img11.gif"
 ALT="$ \;\lambda_1=2,\;\lambda_2=2,\;\lambda_3=0.$">|; 

$key = q/qquadlambda=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="img9.gif"
 ALT="$ \qquad \lambda = 0$">|; 

$key = q/displaystylemathcal{Q}:,2x^2+y^2+z^2-2yz-4y+3z+1=0;;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="356" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="img1.gif"
 ALT="$\displaystyle \mathcal{Q}: \,2x^2+y^2+z^2-2yz-4y+3z+1=0;
$">|; 

$key = q/quadlambda=2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="img10.gif"
 ALT="$ \quad \lambda
= 2$">|; 

$key = q/displaystylemathcal{Q}:;2x^2+2y^2-displaystylefrac{1}{sqrt{2}}z=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="215" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="img14.gif"
 ALT="$\displaystyle \mathcal{Q}:\;2x^2+2y^2-\displaystyle \frac{1}{\sqrt{2}}z=0
$">|; 

1;

