# LaTeX2HTML 99.1 release (March 30, 1999)
# Associate images original text with physical files.


$key = q/;mathcal{Q};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="img3.gif"
 ALT="$ \;\mathcal{Q}$">|; 

$key = q/displaystyle(1,0,0);;(0,1,-1);(0,1,1).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="222" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="img10.gif"
 ALT="$\displaystyle (1,0,0); \;(0,1,-1) \;(0,1,1). $">|; 

$key = q/{displaymath}Longrightarrow;widetilde{mathcal{M}}=frac{textstyle1}{textstyle5}leh4}<col_mark>sqrt{5slash8}<row_mark>array{right){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="395" HEIGHT="118" BORDER="0"
 SRC="img19.gif"
 ALT="\begin{displaymath}
\Longrightarrow \; \widetilde{\mathcal{M}} = \frac{\textsty...
...1/2 &amp; 0 &amp; -\sqrt{5/4} &amp; \sqrt{5/8} \\\\
\end{array}
\right)
\end{displaymath}">|; 

$key = q/;widetilde{mathcal{M}};;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="24" ALIGN="BOTTOM" BORDER="0"
 SRC="img16.gif"
 ALT="$ \;\widetilde{\mathcal{M}}\;$">|; 

$key = q/checkmark;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="img20.gif"
 ALT="$ \checkmark $">|; 

$key = q/;mathcal{Q}inA^3(mathbb{R});;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="img1.gif"
 ALT="$ \;\mathcal{Q} \in A^3(\mathbb {R})\;$">|; 

$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="img11.gif"
 ALT="$ \,\mathcal{A}_0$">|; 

$key = q/qquadlambda=4;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 = 4$">|; 

$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="img17.gif"
 ALT="$ \,\mathcal{Q}$">|; 

$key = q/{displaymath}mathcal{M}=left(array{{ccc}1<col_mark>0<col_mark>0<row_mark>0<col_m>y=y'+z'<row_mark>z=-y'+z'<row_mark>array{right.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="364" HEIGHT="90" BORDER="0"
 SRC="img12.gif"
 ALT="\begin{displaymath}
\mathcal{M} = \left(
\begin{array}{ccc}
1 &amp; 0 &amp; 0 \\\\
0...
...\
y = y' + z' \\\\
z = -y'+ z' \\\\
\end{array}
\right.
\end{displaymath}">|; 

$key = q/{displaymath}mathcal{A}:=left(array{{cccc}-4<col_mark>0<col_mark>1<col_mark>-1<rrk>0<col_mark>1<col_mark>3<row_mark>array{right){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="405" HEIGHT="118" BORDER="0"
 SRC="img4.gif"
 ALT="\begin{displaymath}
\mathcal{A}\: = \left(
\begin{array}{cccc}
-4 &amp; 0 &amp; 1 &amp; -...
... 0 \\\\
0 &amp; 3 &amp; 1 \\\\
0 &amp; 1 &amp; 3 \\\\
\end{array}
\right)
\end{displaymath}">|; 

$key = q/{displaymath}left{array{{l}x''=x'<row_mark>y''=y'+displaystylefrac{1}{2}<row_mar8}{<text_mark>style5}(z'')^2-1=0<row_mark>array{{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="493" HEIGHT="100" BORDER="0"
 SRC="img14.gif"
 ALT="\begin{displaymath}
\left\{
\begin{array}{l}
x'' = x' \\\\
y'' = y' +\displa...
...\frac{\textstyle 8}{\textstyle 5}(z'')^2-1=0\\\\
\end{array}
\end{displaymath}">|; 

$key = q/{displaymath}array{{cl},<col_mark>2(x')^2+4(y')^2+8(z')^2+4y'-4=0<row_mark>,<colk>style1}{<text_mark>style2}-2=0<row_mark>array{{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="426" HEIGHT="215" BORDER="0"
 SRC="img13.gif"
 ALT="\begin{displaymath}
\begin{array}{cl}
\, &amp; 2(x')^2+4(y')^2+8(z')^2+4y'-4=0\\\\  ...
...(z')^2-\frac{\textstyle 1}{\textstyle 2}-2=0\\\\
\end{array}
\end{displaymath}">|; 

$key = q/{displaymath}left{array{{clll}x<col_mark>=;x'<col_mark>=;x''<col_mark>=;displaysrt{frac{5}{8}}z'''+1slash2<row_mark>array{right.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="543" HEIGHT="202" BORDER="0"
 SRC="img18.gif"
 ALT="\begin{displaymath}
\left\{
\begin{array}{clll}
x &amp; = \;x' &amp; = \;x'' &amp; = \;\d...
...aystyle\sqrt{\frac{5}{8}}z'''+ 1/2 \\\\
\end{array}
\right.
\end{displaymath}">|; 

$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="img5.gif"
 ALT="$ \;det\mathcal{A} \neq 0 \quad \Rightarrow \quad r(Q)=4
\quad \Rightarrow \mathcal{Q}\;$">|; 

$key = q/{displaymath}array{{ccc}left{array{{l}x'''=displaystylesqrt{frac{2}{5}}x''<row_mbox{immaginario}<row_mark>array{<row_mark>array{{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="562" HEIGHT="202" BORDER="0"
 SRC="img15.gif"
 ALT="\begin{displaymath}
\begin{array}{ccc}
\left\{
\begin{array}{l}
x''' = \disp...
...de}\\\\
\mbox{immaginario}\\\\
\end{array}\\\\
\end{array}
\end{displaymath}">|; 

$key = q/displaystyle2x^2+3y^2+3z^2+2yz+2y-2z-4=0;;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="340" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="img2.gif"
 ALT="$\displaystyle 2x^2+3y^2+3z^2+2yz+2y-2z-4=0;
$">|; 

$key = q/displaystylep(lambda)=det(mathcal{A}_0-lambdaI)=(2-lambda)((3-lambda)^2-1)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="402" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="img7.gif"
 ALT="$\displaystyle p(\lambda)= det(\mathcal{A}_0 - \lambda
I)=(2-\lambda)((3-\lambda)^2-1)=0
$">|; 

$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="img6.gif"
 ALT="$ \,\mathcal{A}_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;

