# LaTeX2HTML 99.1 release (March 30, 1999)
# Associate images original text with physical files.


$key = q/displaystylemathcal{Q}:,3x^2+y^2-z^2+2xy-2x+4z+5=0;;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="358" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="img1.gif"
 ALT="$\displaystyle \mathcal{Q}: \,3x^2+y^2-z^2+2xy-2x+4z+5=0;
$">|; 

$key = q/quadq(X)=,^tXmathcal{A}_0X,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="158" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="img9.gif"
 ALT="$ \quad q(X)= \,^tX \mathcal{A}_0 X
\,$">|; 

$key = q/,v_1,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="img12.gif"
 ALT="$ \,v_1\,$">|; 

$key = q/,v_2,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="img18.gif"
 ALT="$ \,v_2\,$">|; 

$key = q/,v_3,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="img23.gif"
 ALT="$ \,v_3\,$">|; 

$key = q/displaystyle(x')^2-(y')^2+2(z')^2+4y'-2z'+5=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="330" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="img33.gif"
 ALT="$\displaystyle (x')^2-(y')^2+2(z')^2+4y'-2z'+5=0
$">|; 

$key = q/;^t(x,y,z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="img11.gif"
 ALT="$ \;^t(x,y,z)$">|; 

$key = q/;v_3=,^t(1,-1,0);;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="140" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="img26.gif"
 ALT="$ \;v_3=\,^t(1,-1,0)\;$">|; 

$key = q/{displaymath}array{{cl};<col_mark>(x')^2-left((y')^2-4y'+4right)+2left((z')^2-z'rk>style17}{<text_mark>style2}=0<row_mark>array{{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="529" HEIGHT="106" BORDER="0"
 SRC="img36.gif"
 ALT="\begin{displaymath}
\begin{array}{cl}
\; &amp; (x')^2-\left( (y')^2-4y'+4\right)+...
...t)^2+
\frac{\textstyle 17}{\textstyle 2}=0 \\\\
\end{array}
\end{displaymath}">|; 

$key = q/,textbf{q},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="img8.gif"
 ALT="$ \,\textbf{q}\,$">|; 

$key = q/{displaymath}mathcal{M}=left(array{{ccc}0<col_mark>0<col_mark>1<row_mark>1<col_mrk>0<col_mark>1<col_mark>0<row_mark>array{right){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="166" HEIGHT="90" BORDER="0"
 SRC="img31.gif"
 ALT="\begin{displaymath}
\mathcal{M} = \left(
\begin{array}{ccc}
0 &amp; 0 &amp; 1 \\\\
1 &amp; 0 &amp; -1 \\\\
0 &amp; 1 &amp; 0 \\\\
\end{array}
\right)
\end{displaymath}">|; 

$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="img2.gif"
 ALT="$ \,\mathcal{Q}$">|; 

$key = q/{displaymath}left(array{{c}x<row_mark>y<row_mark>z<row_mark>array{right)=mathcalmark>y=x'-z'<row_mark>z=y'<row_mark>array{right.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="349" HEIGHT="90" BORDER="0"
 SRC="img32.gif"
 ALT="\begin{displaymath}
\left(
\begin{array}{c}
x \\\\
y \\\\
z \\\\
\end{arra...
... z' \\\\
y = x' - z' \\\\
z = y' \\\\
\end{array}
\right.
\end{displaymath}">|; 

$key = q/;q(v_3)=2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="img27.gif"
 ALT="$ \;q(v_3)=2$">|; 

$key = q/;mathcal{B}_0=,^tmathcal{M}mathcal{A}_0mathcal{M};;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="138" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="img30.gif"
 ALT="$ \;\mathcal{B}_0=\,^t\mathcal{M}\mathcal{A}_0 \mathcal{M} \;$">|; 

$key = q/{displaymath}mathcal{B}_0:=left(array{{ccc}1<col_mark>0<col_mark>0<row_mark>0<cork>0<col_mark>0<col_mark>2<row_mark>array{right){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="168" HEIGHT="90" BORDER="0"
 SRC="img29.gif"
 ALT="\begin{displaymath}
\mathcal{B}_0\: = \left(
\begin{array}{ccc}
1 &amp; 0 &amp; 0 \\\\
0 &amp; -1 &amp; 0 \\\\
0 &amp; 0 &amp; 2 \\\\
\end{array}
\right)
\end{displaymath}">|; 

$key = q/{displaymath}e_2^{perp}:;(0,1,0)mathcal{A}_0left(array{{c}x<row_mark>y<row_mark><row_mark>array{right)=0quadRightarrowquadx+y=0.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="371" HEIGHT="90" BORDER="0"
 SRC="img17.gif"
 ALT="\begin{displaymath}
e_2^{\perp}: \;(0,1,0)\mathcal{A}_0 \left(
\begin{array}{c...
...
\end{array}
\right) = 0 \quad \Rightarrow \quad x + y = 0.
\end{displaymath}">|; 

$key = q/,y',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="img34.gif"
 ALT="$ \,y'\,$">|; 

$key = q/,mathcal{Q},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="img5.gif"
 ALT="$ \,\mathcal{Q} \,$">|; 

$key = q/;e_3^{perp}:;z=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="img22.gif"
 ALT="$ \;e_3^{\perp}
:\;z=0$">|; 

$key = q/;q(e_2)=1;;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="img15.gif"
 ALT="$ \;q(e_2)=1\;$">|; 

$key = q/,X;;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="img10.gif"
 ALT="$ \,X\;$">|; 

$key = q/{displaymath}quadleft{array{{l}x''=x'<row_mark>y''=y'-2<row_mark>z''=z'-frac{<testyle1}{<text_mark>style2}<row_mark>array{right.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="114" HEIGHT="91" BORDER="0"
 SRC="img37.gif"
 ALT="\begin{displaymath}\quad \left\{
\begin{array}{l}
x'' = x' \\\\
y'' = y' - 2 ...
...- \frac{\textstyle 1}{\textstyle 2} \\\\
\end{array} \right.
\end{displaymath}">|; 

$key = q/;e_2=,^t(0,1,0);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="120" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="img14.gif"
 ALT="$ \;e_2=\,^t(0,1,0)$">|; 

$key = q/quadq(v_3)neq0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="98" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="img25.gif"
 ALT="$ \quad q(v_3) \neq 0$">|; 

$key = q/;q(e_3)=-1;;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="img21.gif"
 ALT="$ \;q(e_3)=-1\;$">|; 

$key = q/{displaymath}mathcal{A}:=left(array{{cccc}5<col_mark>-1<col_mark>0<col_mark>2<rok>0<col_mark>0<col_mark>-1<row_mark>array{right){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="435" HEIGHT="118" BORDER="0"
 SRC="img3.gif"
 ALT="\begin{displaymath}
\mathcal{A}\: = \left(
\begin{array}{cccc}
5 &amp; -1 &amp; 0 &amp; 2...
...0 \\\\
1 &amp; 1 &amp; 0 \\\\
0 &amp; 0 &amp; -1 \\\\
\end{array}
\right)
\end{displaymath}">|; 

$key = q/{displaymath}array{{cl};<col_mark>(x'')^2-(y'')^2+2(z'')^2+frac{<text_mark>style}{<text_mark>style17}(z'')^2-1=0<row_mark>array{{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="348" HEIGHT="91" BORDER="0"
 SRC="img38.gif"
 ALT="\begin{displaymath}
\begin{array}{cl}
\; &amp; (x'')^2-(y'')^2+2(z'')^2+\frac{\te...
...rac{\textstyle 4}{\textstyle 17}(z'')^2-1=0 \\\\
\end{array}
\end{displaymath}">|; 

$key = q/,z';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="img35.gif"
 ALT="$ \,z'$">|; 

$key = q/;beta=(e_2,e_3,v_3);;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="132" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="img28.gif"
 ALT="$ \;\beta=(e_2,e_3,v_3)\;$">|; 

$key = q/,mathcal{D},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="img6.gif"
 ALT="$ \,\mathcal{D} \,$">|; 

$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="img4.gif"
 ALT="$ \;det\mathcal{A} \neq 0 \quad \Rightarrow \quad r(Q)=4
\quad \Rightarrow \mathcal{Q}\;$">|; 

$key = q/;v_3ine_2^{perp}cape_3^{perp};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="img24.gif"
 ALT="$ \;v_3 \in e_2^{\perp} \cap e_3^{\perp}$">|; 

$key = q/;q(v_1)neq0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="img13.gif"
 ALT="$ \;q(v_1) \neq 0$">|; 

$key = q/;q(v_2)neq0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="img19.gif"
 ALT="$ \;q(v_2) \neq
0$">|; 

$key = q/;e_3=,^t(0,0,1);quade_3ine_2^{perp};;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="212" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="img20.gif"
 ALT="$ \;e_3=\,^t(0,0,1);\quad e_3 \in e_2^{\perp}\;$">|; 

$key = q/;e_2^{perp};;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="img16.gif"
 ALT="$ \;e_2^{\perp}\;$">|; 

$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="img7.gif"
 ALT="$ \,\mathcal{A}_0 \,$">|; 

1;

