# LaTeX2HTML 99.1 release (March 30, 1999)
# Associate images original text with physical files.


$key = q/:cinA^3(K):;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="98" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="img24.gif"
 ALT="$ \:c \in
A^3(K)\: $">|; 

$key = q/{displaymath}array{{lcl}mathcal{A}=left(array{{cc}a_{00}<col_mark>^tlambda<row_mambda=,^t(a_{10},a_{20},a_{30});<row_mark>array{{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="377" HEIGHT="64" BORDER="0"
 SRC="img14.gif"
 ALT="\begin{displaymath}
\begin{array}{lcl}
\mathcal{A} = \left(
\begin{array}{cc}...
...e &amp;
\;\lambda = \,^t(a_{10},a_{20},a_{30});\\\\
\end{array}
\end{displaymath}">|; 

$key = q/,g,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="img7.gif"
 ALT="$ \,g\,$">|; 

$key = q/displaystylemathcal{A}_0,c+lambda=0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="112" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="img23.gif"
 ALT="$\displaystyle \mathcal{A}_0\, c +
\lambda = 0.$">|; 

$key = q/,i=1,2,3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="img5.gif"
 ALT="$ \,i = 1,2,3$">|; 

$key = q/{displaymath}left(array{{cc}b_{00}<col_mark>^tlambda'<row_mark>lambda'<col_mark>5mm}lambda'=:^tmathcal{M}(mathcal{A}_0,c+lambda){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="341" HEIGHT="64" BORDER="0"
 SRC="img18.gif"
 ALT="\begin{displaymath}\left(
\begin{array}{cc}
b_{00} &amp; ^t\lambda' \\\\
\lambda'...
...{5mm}\lambda' =
\:^t\mathcal{M}(\mathcal{A}_0\, c + \lambda)
\end{displaymath}">|; 

$key = q/displaystyleg(x,y,z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="img8.gif"
 ALT="$\displaystyle g(x,y,z)$">|; 

$key = q/displaystyle=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="img9.gif"
 ALT="$\displaystyle =$">|; 

$key = q/:mathcal{A}_0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="img25.gif"
 ALT="$ \:\mathcal{A}_0 \,$">|; 

$key = q/:^tmathcal{M};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="img22.gif"
 ALT="$ \:^t\mathcal{M}$">|; 

$key = q/,i=1,2,3,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="img19.gif"
 ALT="$ \,i = 1,2,3
\,$">|; 

$key = q/,mathcal{B},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="img17.gif"
 ALT="$ \,\mathcal{B} \,$">|; 

$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="img15.gif"
 ALT="$ \,\mathcal{Q}$">|; 

$key = q/{displaymath}widetilde{mathcal{M}}=left(array{{cc}1<col_mark>0<row_mark>c<col_mamm}c=;^t(c_1,,c_2,,c_3),quadmathcal{M}inGL_3(K).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="501" HEIGHT="64" BORDER="0"
 SRC="img16.gif"
 ALT="\begin{displaymath}
\widetilde{\mathcal{M}} = \left(
\begin{array}{cc}
1 &amp; 0 ...
...m} c = \;^t(c_1,\,c_2,\,c_3),
\quad \mathcal{M} \in GL_3(K).
\end{displaymath}">|; 

$key = q/,c,v_1,v_2,v_3,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="img2.gif"
 ALT="$ \,c,v_1,v_2,v_3 \,$">|; 

$key = q/mathcal{B}:=hspace{2mm}^twidetilde{mathcal{M}}hspace{1mm}mathcal{A}hspace{1mm}widetilde{mathcal{M}}:;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="136" HEIGHT="24" ALIGN="BOTTOM" BORDER="0"
 SRC="img13.gif"
 ALT="$ \mathcal{B}\: =
\hspace{2mm} ^t\widetilde{\mathcal{M}} \hspace{1mm} \mathcal{A}
\hspace{1mm} \widetilde{\mathcal{M}}\:$">|; 

$key = q/,mathcal{B}=b_{ij},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="img3.gif"
 ALT="$ \,\mathcal{B} = b_{ij}\,$">|; 

$key = q/displaystyleg(-x,-y,-z).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="125" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="img12.gif"
 ALT="$\displaystyle g(-x,-y,-z).$">|; 

$key = q/,b_{i0}=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="img4.gif"
 ALT="$ \,b_{i0} = 0 \,$">|; 

$key = q/displaystyleb_{11}(x)^2+b_{22}(y)^2+b_{33}(z)^2+2b_{12}xy+2b_{13}xz+b_{23}yz+b_{00};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="474" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="img10.gif"
 ALT="$\displaystyle b_{11}(x)^2+b_{22}(y)^2+b_{33}(z)^2+2b_{12}xy+2b_{13}xz+b_{23}yz+b_{00}$">|; 

$key = q/displaystyle^tmathcal{M}(mathcal{A}_0,c+lambda)=lambda'=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="191" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="img20.gif"
 ALT="$\displaystyle ^t\mathcal{M}(\mathcal{A}_0\, c + \lambda) = \lambda' = 0
$">|; 

$key = q/:mathcal{M};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="img21.gif"
 ALT="$ \:\mathcal{M}$">|; 

$key = q/displaystyleb_{11}(-x)^2+b_{22}(-y)^2+b_{33}(-z)^2+2b_{12}(-x)(-y)+cdots+b_{00};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="483" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="img11.gif"
 ALT="$\displaystyle b_{11}(-x)^2+b_{22}(-y)^2+b_{33}(-z)^2+2b_{12}(-x)(-y)+ \cdots +b_{00}$">|; 

$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="img1.gif"
 ALT="$ \,\mathcal{Q} \,$">|; 

$key = q/,c,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="img6.gif"
 ALT="$ \,c\,$">|; 

1;

