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


$key = q/mathrmMtextbf{x};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img17.png"
 ALT="$\mathrm
M\textbf{x}$">|; 

$key = q/mathrmA^2_{infty};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img4.png"
 ALT="$\mathrm A^2_{\infty}$">|; 

$key = q/{displaymath}textbfx^tmathrmM^tmathrmAmathrmMtextbfx=0,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="114" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img18.png"
 ALT="\begin{displaymath}
\textbf x^t\mathrm M^t\mathrm A\mathrm M\textbf x=0,
\end{displaymath}">|; 

$key = q/mathrmB=mathrmM^tmathrmAmathrmM;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img20.png"
 ALT="$\mathrm B=\mathrm M^t\mathrm A\mathrm M$">|; 

$key = q/a_{21}=a_{12};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img10.png"
 ALT="$a_{21}=a_{12}$">|; 

$key = q/{displaymath}a_{11}x_1^2+2a_{12}x_1x_2+a_{22}x_2^2+2a_{01}x_0x_1+2a_{02}x_0x_2+a_{33}x_0^2=0,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="467" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img7.png"
 ALT="\begin{displaymath}
a_{11}x_1^2+2a_{12}x_1x_2+a_{22}x_2^2+2a_{01}x_0x_1+2a_{02}x_0x_2+a_{33}x_0^2=0,
\end{displaymath}">|; 

$key = q/a_{13}=a_{31};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img11.png"
 ALT="$a_{13}=a_{31}$">|; 

$key = q/a_{ij}inmathbfR;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img8.png"
 ALT="$a_{ij}\in \mathbf R$">|; 

$key = q/{displaymath}textbfx^tmathrmBtextbfx=0,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img19.png"
 ALT="\begin{displaymath}
\textbf x^t\mathrm B\textbf x=0,
\end{displaymath}">|; 

$key = q/mathcalC;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img6.png"
 ALT="$\mathcal C$">|; 

$key = q/left(array{{c}x_0x_1x_2array{right);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="83" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img14.png"
 ALT="$\left( \begin{array}{c}
x_0\\\\
x_1\\\\
x_2
\end{array} \right)$">|; 

$key = q/mathrmM;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img15.png"
 ALT="$\mathrm M$">|; 

$key = q/mathbfR;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2.png"
 ALT="$\mathbf R$">|; 

$key = q/mathrmP^2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3.png"
 ALT="$\mathrm P^2$">|; 

$key = q/a_{23}=a_{32};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img12.png"
 ALT="$a_{23}=a_{32}$">|; 

$key = q/(3times3);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img16.png"
 ALT="$(3\times3)$">|; 

$key = q/{displaymath}textbf{x}^tmathrmAtextbf{x}=0,{displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img13.png"
 ALT="\begin{displaymath}
\textbf{x}^t\mathrm A\textbf{x}=0,
\end{displaymath}">|; 

$key = q/mathrmA^2;MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img5.png"
 ALT="$\mathrm A^2$">|; 

$key = q/{displaymath}mathrmA=left(array{{ccc}a_{00}&a_{01}&a_{02}a_{10}&a_{11}&a_{12}a_{20}&a_{21}&a_{22}array{right){displaymath};MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="178" HEIGHT="73" BORDER="0"
 SRC="|."$dir".q|img9.png"
 ALT="\begin{displaymath}
\mathrm A=\left(
\begin{array}{ccc}
a_{00} &amp; a_{01} &amp; a_{...
...} &amp; a_{12}\\\\
a_{20} &amp; a_{21} &amp; a_{22}
\end{array}
\right)
\end{displaymath}">|; 

$key = q/mathrmP^2(mathbfR);MSF=1.6;LFS=11;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1.png"
 ALT="$\mathrm P^2(\mathbf R)$">|; 

1;

