# LaTeX2HTML 99.1 release (March 30, 1999)
# Associate images original text with physical files.


$key = q/quadv=(0,1,-1);;;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="143" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="img12.gif"
 ALT="$ \quad
v=(0,1,-1);\;$">|; 

$key = q/displaystylefrac{textstylex^2}{textstylea_1^2}+frac{textstyley^2}{textstylea_2^2}-2z=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="148" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="img29.gif"
 ALT="$\displaystyle \frac{\textstyle x^2}{\textstyle a_1^2}+\frac{\textstyle
y^2}{\textstyle a_2^2}-2z=0
$">|; 

$key = q/{displaymath}left(array{{c}x<row_mark>y<row_mark>z<row_mark>array{right)=mathcallefrac{1}{sqrt{2}}(-y'+z')<row_mark>array{right.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="406" HEIGHT="179" BORDER="0"
 SRC="img21.gif"
 ALT="\begin{displaymath}
\left(
\begin{array}{c}
x \\\\
y \\\\
z \\\\
\end{arra...
...aystyle\frac{1}{\sqrt{2}}(-y'+ z') \\\\
\end{array}
\right.
\end{displaymath}">|; 

$key = q/quad2(x''')^2+2(y''')^2-frac{textstyle1}{sqrt{textstyle2}}z'''=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="262" HEIGHT="48" ALIGN="MIDDLE" BORDER="0"
 SRC="img28.gif"
 ALT="$ \quad
2(x''')^2+2(y''')^2-\frac{\textstyle 1}{\sqrt{\textstyle 2}}
z'''=0 $">|; 

$key = q/{displaymath}V_2:;left(array{{ccc}0<col_mark>0<col_mark>0<row_mark>0<col_mark>-1=0qquadRightarrowy+z=0quadLeftrightarrowquadz=-y{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="545" HEIGHT="90" BORDER="0"
 SRC="img10.gif"
 ALT="\begin{displaymath}
V_2:\; \left(
\begin{array}{ccc}
0 &amp; 0 &amp; 0 \\\\
0 &amp; -1 &amp;...
... 0 \qquad \Rightarrow y+z=0 \quad \Leftrightarrow \quad
z=-y
\end{displaymath}">|; 

$key = q/{displaymath}left{array{{l}x''=x'<row_mark>y''=y'-frac{<text_mark>style7}{<text_textstyle33sqrt{textstyle2}}{textstyle16}right)}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="511" HEIGHT="138" BORDER="0"
 SRC="img25.gif"
 ALT="\begin{displaymath}
\left\{
\begin{array}{l}
x'' = x' \\\\
y'' = y' - \frac{...
...frac{\textstyle 33\sqrt{\textstyle 2}}{\textstyle 16}\right)}
\end{displaymath}">|; 

$key = q/quadV_0:;x=0;;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="img14.gif"
 ALT="$ \quad V_0: \;x=0 \;$">|; 

$key = q/{displaymath}array{{ccc}left{array{{l}bar{x}=sqrt{2}x'''<row_mark>bar{y}=sqrt{2}>mbox{ellittico}<row_mark>array{<row_mark>array{{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="460" HEIGHT="99" BORDER="0"
 SRC="img27.gif"
 ALT="\begin{displaymath}
\begin{array}{ccc}
\left\{
\begin{array}{l}
\bar{x} = \s...
...oide}\\\\
\mbox{ellittico}\\\\
\end{array}\\\\
\end{array}
\end{displaymath}">|; 

$key = q/{displaymath}left{array{{l}x'''=x''<row_mark>y'''=y''<row_mark>z'''=z''+frac{<tey''')^2-frac{textstyle1}{sqrt{textstyle2}}z'''=0{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="491" HEIGHT="99" BORDER="0"
 SRC="img26.gif"
 ALT="\begin{displaymath}
\left\{
\begin{array}{l}
x''' = x'' \\\\
y''' = y'' \\\\  ...
...^2+2(y''')^2-\frac{\textstyle 1}{\sqrt{\textstyle 2}}
z'''=0
\end{displaymath}">|; 

$key = q/checkmark;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="img31.gif"
 ALT="$ \checkmark $">|; 

$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="img8.gif"
 ALT="$ \qquad \lambda = 0$">|; 

$key = q/{displaymath}mathcal{M}=left(array{{ccc}1<col_mark>0<col_mark>0<row_mark>0<col_m{2}<col_mark>1slashsqrt{2}<row_mark>array{right){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="236" HEIGHT="90" BORDER="0"
 SRC="img20.gif"
 ALT="\begin{displaymath}
\mathcal{M} = \left(
\begin{array}{ccc}
1 &amp; 0 &amp; 0 \\\\
0...
...\\\\
0 &amp; -1/\sqrt{2} &amp; 1/\sqrt{2} \\\\
\end{array}
\right)
\end{displaymath}">|; 

$key = q/,y';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="img23.gif"
 ALT="$ \,y'$">|; 

$key = q/displaystyle2(x')^2+2underbrace{left((y')^2-frac{textstyle7}{2sqrt{textstyle2}}ytyle1}{sqrt{textstyle2}}z'-frac{textstyle49}{textstyle16}+1=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="447" HEIGHT="160" ALIGN="MIDDLE" BORDER="0"
 SRC="img24.gif"
 ALT="$\displaystyle 2(x')^2+2\underbrace{\left( (y')^2-\frac{\textstyle
7}{2\sqrt{\t...
...\textstyle 1}{\sqrt{\textstyle
2}}z'-\frac{\textstyle 49}{\textstyle 16}+1=0
$">|; 

$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="img5.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/,mathcal{A}_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="img19.gif"
 ALT="$ \,\mathcal{A}_0$">|; 

$key = q/,mathcal{Q};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="img4.gif"
 ALT="$ \,\mathcal{Q} $">|; 

$key = q/>1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="img17.gif"
 ALT="$ &gt; 1$">|; 

$key = q/;V_2=<e_1,v>;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="122" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="img13.gif"
 ALT="$ \;V_2 = &lt;e_1,v&gt;$">|; 

$key = q/;y=z;quadRightarrowquadV_0=<w>;;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="222" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="img15.gif"
 ALT="$ \;
y=z; \quad \Rightarrow \quad V_0=&lt;w&gt;\;$">|; 

$key = q/;detmathcal{A}neq0quadRightarrowquadr(Q)=4quadRightarrowmathcal{Q};;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="294" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="img6.gif"
 ALT="$ \;det\mathcal{A} \neq 0 \quad \Rightarrow \quad r(Q)=4
\quad \Rightarrow \mathcal{Q}\;$">|; 

$key = q/displaystylep(lambda)=det(mathcal{A}_0-lambdaI)=(2-lambda)((1-lambda)^2-1)=(2-lambda)^2lambda=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="504" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="img7.gif"
 ALT="$\displaystyle p(\lambda)= det(\mathcal{A}_0 - \lambda
I)=(2-\lambda)((1-\lambda)^2-1)=(2-\lambda)^2\lambda=0
$">|; 

$key = q/,mathcal{M},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="img2.gif"
 ALT="$ \,\mathcal{M}\,$">|; 

$key = q/quade_1=(1,0,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="124" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="img11.gif"
 ALT="$ \quad e_1=(1,0,0)$">|; 

$key = q/;beta=(e_1,v,w);;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="123" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="img18.gif"
 ALT="$ \;\beta=(e_1,v,w)\;$">|; 

$key = q/quadw=(0,1,1);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="122" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="img16.gif"
 ALT="$ \quad w=(0,1,1)
$">|; 

$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="img1.gif"
 ALT="$ \,\mathcal{A}_0\,$">|; 

$key = q/displaystylefrac{textstyle(x''')^2}{frac{textstyle1}{textstyle4sqrt{2}}}+frac{textstyle(y''')^2}{frac{textstyle1}{textstyle4sqrt{2}}}-2z=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="200" HEIGHT="76" ALIGN="MIDDLE" BORDER="0"
 SRC="img30.gif"
 ALT="$\displaystyle \frac{\textstyle (x''')^2}{\frac{\textstyle 1}{\textstyle
4\sqrt...
...+ \frac{\textstyle (y''')^2}{\frac{\textstyle
1}{\textstyle 4\sqrt{2}}}-2z=0
$">|; 

$key = q/displaystyle2(x')^2+2(y')^2-frac{textstyle7}{sqrt{textstyle2}}y'-frac{textstyle1}{sqrt{textstyle2}}z'+1=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="320" HEIGHT="58" ALIGN="MIDDLE" BORDER="0"
 SRC="img22.gif"
 ALT="$\displaystyle 2(x')^2+2(y')^2-\frac{\textstyle 7}{\sqrt{\textstyle 2}} y'-
\frac{\textstyle 1}{\sqrt{\textstyle 2}}z'+1=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="img3.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="img9.gif"
 ALT="$ \quad \lambda = 2$">|; 

1;

