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


$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="|."$dir".q|img13.png"
 ALT="$\mathbf R^2$">|; 

$key = q/%latex2htmlidmarker181includegraphics[width=9cm,height=14cm]{esercizio3.eps};LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="396" HEIGHT="627" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img22.png"
 ALT="% latex2html id marker 181
\includegraphics[width=9cm,height=14cm]{esercizio3.eps}">|; 

$key = q/(mathcalA_0-mathcalI)X=0;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img6.png"
 ALT="$(\mathcal A_0-\mathcal I)X=0$">|; 

$key = q/left(array{{c}xyarray{right)=mathcalPleft(array{{c}XYarray{right)=left(array{{c}lefrac{1}{sqrt{2}}X+displaystylefrac{1}{sqrt{2}}Yarray{right);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="338" HEIGHT="103" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img15.png"
 ALT="$\left(
\begin{array}{c}
x\\\\
y
\end{array}
\right)=\mathcal P \left(
\b...
...style\frac{1}{\sqrt{2}}X+\displaystyle\frac{1}{\sqrt{2}}Y
\end{array}
\right)$">|; 

$key = q/{displaymath}X^2+5Y^2+displaystylefrac{32}{sqrt{2}}X+7=0.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="205" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img17.png"
 ALT="\begin{displaymath}
X^2+5Y^2+\displaystyle\frac{32}{\sqrt{2}}X+7=0.
\end{displaymath}">|; 

$key = q/{displaymath}x^2+5y^2-121=0,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="148" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img21.png"
 ALT="\begin{displaymath}
x^2+5y^2-121=0,
\end{displaymath}">|; 

$key = q/(1,-1)inV_{1};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img8.png"
 ALT="$(1,-1)\in V_{1}$">|; 

$key = q/V_5=V_{1}^bot;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img10.png"
 ALT="$V_5=V_{1}^\bot$">|; 

$key = q/v_1=displaystylefrac{1}{sqrt2}(1,-1);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="123" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img9.png"
 ALT="$v_1=\displaystyle\frac{1}{\sqrt 2}(1,-1)$">|; 

$key = q/mathcalA_0-mathcalI=left(array{{cc}2&22&2array{right);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="156" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img5.png"
 ALT="$\mathcal A_0-\mathcal I=\left(
\begin{array}{cc}
2 &amp; 2\\\\
2 &amp; 2
\end{array}
\right)$">|; 

$key = q/{displaymath}x^2+5y^2-(2alpha-displaystylefrac{32}{sqrt{2}})x-10betay+alpha^2+5beta^2-displaystylefrac{32}{sqrt{2}}alpha+7=0.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="450" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img19.png"
 ALT="\begin{displaymath}
x^2+5y^2-(2\alpha-\displaystyle\frac{32}{\sqrt{2}})x-10\bet...
...\alpha^2+5\beta^2-\displaystyle\frac{32}{\sqrt{2}}\alpha+7=0.
\end{displaymath}">|; 

$key = q/{displaymath}left{array{{cc}alpha=displaystylefrac{16}{sqrt{2}}beta=0array{right.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="67" BORDER="0"
 SRC="|."$dir".q|img20.png"
 ALT="\begin{displaymath}
\left \{
\begin{array}{cc}
\alpha=\displaystyle\frac{16}{\sqrt{2}}\\\\
\beta=0
\end{array}
\right.
\end{displaymath}">|; 

$key = q/q(x,y)=3x^2+4xy+3y^2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="199" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1.png"
 ALT="$q(x,y)=3x^2+4xy+3y^2$">|; 

$key = q/{displaymath}X^2+5Y^2+16(displaystylefrac{1}{sqrt{2}}X+displaystylefrac{1}{sqrt{1}{sqrt{2}}X+displaystylefrac{1}{sqrt{2}}Y)+7=0,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="469" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img16.png"
 ALT="\begin{displaymath}
X^2+5Y^2+16(\displaystyle\frac{1}{\sqrt{2}}X+\displaystyle\...
...yle\frac{1}{\sqrt{2}}X+\displaystyle\frac{1}{\sqrt{2}}Y)+7=0,
\end{displaymath}">|; 

$key = q/{displaymath}mathcalP=displaystylefrac{1}{sqrt2}left(array{{rr}1&1-1&1array{right).{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="161" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img14.png"
 ALT="\begin{displaymath}
\mathcal P=\displaystyle\frac{1}{\sqrt2} \left(
\begin{array}{rr}
1 &amp;1\\\\
-1 &amp; 1
\end{array}
\right).
\end{displaymath}">|; 

$key = q/{displaymath}mathcalA_0=left(array{{cc}3&22&3array{right).{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="126" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img2.png"
 ALT="\begin{displaymath}
\mathcal A_0= \left(
\begin{array}{cc}
3 &amp; 2\\\\
2 &amp; 3
\end{array}
\right).
\end{displaymath}">|; 

$key = q/v_2=displaystylefrac{1}{sqrt2}(1,1);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="109" HEIGHT="54" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img11.png"
 ALT="$v_2=\displaystyle\frac{1}{\sqrt2}(1,1)$">|; 

$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="|."$dir".q|img7.png"
 ALT="$X\in\mathbf R^2$">|; 

$key = q/p(lambda)=lambda^2-6lambda+5;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="148" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3.png"
 ALT="$p(\lambda)=\lambda^2-6\lambda+5$">|; 

$key = q/{displaymath}left{array{{cc}X=x-alphaY=y-betaarray{right.{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img18.png"
 ALT="\begin{displaymath}
\left \{
\begin{array}{cc}
X=x-\alpha\\\\
Y=y-\beta
\end{array}
\right.
\end{displaymath}">|; 

$key = q/lambda_1=1,lambda_2=5;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="112" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4.png"
 ALT="$\lambda_1=1, \lambda_2=5$">|; 

$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="|."$dir".q|img12.png"
 ALT="$V=\{v_1, v_2\}$">|; 

1;

