# LaTeX2HTML 2002 (1.62)
# Associate images original text with physical files.


$key = q/(mathcalA-10mathcalI)X=0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="129" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img10.png"
 ALT="$(\mathcal A-10\mathcal I)X=0$">|; 

$key = q/mathbfR^2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1.png"
 ALT="$\mathbf R^2$">|; 

$key = q/V_{10};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img13.png"
 ALT="$V_{10}$">|; 

$key = q/left(array{{c}xyarray{right)=mathcalP^{-1}left(array{{c}xietaarray{right)=mathcatylefrac{1}{sqrt{5}}left(array{{c}2xi+eta-xi+2etaarray{right);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="415" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img27.png"
 ALT="$\left(
\begin{array}{c}
x\\\\
y
\end{array}
\right)=\mathcal P^{-1} \left(
...
...qrt{5}}\left(
\begin{array}{c}
2\xi+\eta\\\\
-\xi+2\eta
\end{array}
\right)$">|; 

$key = q/(x,y)inmathbfR^2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img20.png"
 ALT="$(x,y)\in\mathbf R^2$">|; 

$key = q/includegraphics[width=5.5cm,height=7cm]{es1assi.ps};LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="249" HEIGHT="317" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img32.png"
 ALT="\includegraphics[width=5.5cm,height=7cm]{es1assi.ps}">|; 

$key = q/v_1=displaystylefrac{1}{sqrt5}(2,1);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="109" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img15.png"
 ALT="$v_1=\displaystyle\frac{1}{\sqrt 5}(2,1)$">|; 

$key = q/mathcalP;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img25.png"
 ALT="$\mathcal P$">|; 

$key = q/lambda_1=10,lambda_2=5;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="120" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img8.png"
 ALT="$\lambda_1=10,
\lambda_2=5$">|; 

$key = q/mathcalP=mathcalM_{ev}(id)=displaystylefrac{1}{sqrt5}left(array{{lr}2&-11&2array{right);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="246" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img21.png"
 ALT="$\mathcal
P=\mathcal M_{ev}(id)=\displaystyle\frac{1}{\sqrt5} \left(
\begin{array}{lr}
2 &amp;-1\\\\
1 &amp; 2
\end{array}
\right)$">|; 

$key = q/q(x,y)=9x^2+4xy+6y^2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="199" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3.png"
 ALT="$q(x,y)=9x^2+4xy+6y^2$">|; 

$key = q/XinmathbfR^2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img11.png"
 ALT="$X\in\mathbf R^2$">|; 

$key = q/mathcalA;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img6.png"
 ALT="$\mathcal A$">|; 

$key = q/V={v_1,v_2};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img19.png"
 ALT="$V=\{v_1, v_2\}$">|; 

$key = q/v_2=displaystylefrac{1}{sqrt5}(-1,2);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="123" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img18.png"
 ALT="$v_2=\displaystyle\frac{1}{\sqrt5}(-1,2)$">|; 

$key = q/V_5=V_{10}^bot;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img17.png"
 ALT="$V_5=V_{10}^\bot$">|; 

$key = q/lambda_1=10;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img14.png"
 ALT="$\lambda_1=10$">|; 

$key = q/left(array{{c}xyarray{right);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img24.png"
 ALT="$
\left(
\begin{array}{c}
x\\\\
y
\end{array}
\right)$">|; 

$key = q/V;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img22.png"
 ALT="$V$">|; 

$key = q/<v_1>,<v_2>;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img31.png"
 ALT="$&lt;v_1&gt;, &lt;v_2&gt;$">|; 

$key = q/xi,eta;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img23.png"
 ALT="$\xi, \eta$">|; 

$key = q/lambda_2=5;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img16.png"
 ALT="$\lambda_2=5$">|; 

$key = q/{displaymath}mathcalA=left(array{{lr}9&22&6array{right),{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img4.png"
 ALT="\begin{displaymath}
\mathcal A= \left(
\begin{array}{lr}
9 &amp; 2\\\\
2 &amp; 6
\end{array}
\right),
\end{displaymath}">|; 

$key = q/p_mathcalA(lambda)=lambda^2-15lambda+50;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="177" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img7.png"
 ALT="$p_\mathcal
A(\lambda)=\lambda^2-15\lambda+50$">|; 

$key = q/{displaymath}displaystyleQ_mathcalA(xi,eta)=10xi^2+5eta^2=10left(frac{2x+y}{sqrt5}right)^2+5left(frac{-x+2y}{sqrt5}right)^2.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="432" HEIGHT="49" BORDER="0"
 SRC="|."$dir".q|img28.png"
 ALT="\begin{displaymath}
\displaystyle Q_\mathcal
A(\xi,\eta)=10\xi^2+5\eta^2=10\le...
...x+y}{\sqrt
5}\right)^2+5\left(\frac{-x+2y}{\sqrt5}\right)^2.
\end{displaymath}">|; 

$key = q/(2,1)inV_{10};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img12.png"
 ALT="$(2,1)\in V_{10}$">|; 

$key = q/9x^2+4xy+6y^2=10;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="167" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2.png"
 ALT="$9x^2+4xy+6y^2=10$">|; 

$key = q/displaystylexi^2+frac{eta^2}{2}=1;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="60" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img30.png"
 ALT="$\displaystyle\xi^2+\frac{\eta^2}{2}=1$">|; 

$key = q/includegraphics[width=6cm,height=17cm]{es1ellisse.eps};LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="268" HEIGHT="762" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img33.png"
 ALT="\includegraphics[width=6cm,height=17cm]{es1ellisse.eps}">|; 

$key = q/(mathcalA-10mathcalI)=left(array{{rc}-1&22&4array{right);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="193" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img9.png"
 ALT="$(\mathcal A-10\mathcal I)=\left(
\begin{array}{rc}
-1 &amp; 2\\\\
2 &amp; 4
\end{array}
\right)$">|; 

$key = q/mathcalP^{-1}=mathcalP^t;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img26.png"
 ALT="$\mathcal P^{-1}=\mathcal P^t$">|; 

$key = q/q=Q_mathcal{A};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img5.png"
 ALT="$q=Q_\mathcal{A}$">|; 

$key = q/10xi^2+5eta^2=10;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="125" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img29.png"
 ALT="$10\xi^2+5\eta^2=10$">|; 

1;