# LaTeX2HTML 99.1 release (March 30, 1999)
# Associate images original text with physical files.


$key = q/displaystylewidetilde{mathcal{M}}=left(array{{cccc}1<col_mark>0<col_mark>0<col_m>m_{31}<col_mark>m_{32}<col_mark>m_{33}<row_mark>array{right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="257" HEIGHT="128" ALIGN="MIDDLE" BORDER="0"
 SRC="img14.gif"
 ALT="$\displaystyle \widetilde{\mathcal{M}} = \left(
 \begin{array}{cccc}
 1 &amp; 0 &amp; 0 ...
...&amp; m_{22} &amp; m_{23}\\\\  
 c_3 &amp; m_{31} &amp; m_{32} &amp; m_{33}\\\\  
 \end{array}
 \right)$">|; 

$key = q/xprime,yprimee,zprime;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="img10.gif"
 ALT="$ x\prime,y\prime e\, z\prime$">|; 

$key = q/displaystylemathcal{B}_0=hspace{2mm}^tmathcal{M}hspace{1mm}mathcal{A}_0hspace{1mm}mathcal{M};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="142" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="img19.gif"
 ALT="$\displaystyle \mathcal{B}_0 = \hspace{2mm} ^t\mathcal{M}
 \hspace{1mm} \mathcal{A}_0 \hspace{1mm} \mathcal{M}$">|; 

$key = q/displaystyleleft(array{{cccc}1<col_mark>x'<col_mark>y'<col_mark>z'<row_mark>arra1<row_mark>x'<row_mark>y'<row_mark>z'<row_mark>array{right)=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="262" HEIGHT="128" ALIGN="MIDDLE" BORDER="0"
 SRC="img15.gif"
 ALT="$\displaystyle \left(
 \begin{array}{cccc}
 1 &amp; x' &amp; y' &amp; z'\\\\  
 \end{array}
 \...
... \left(
 \begin{array}{c}
 1 \\\\  x' \\\\  y' \\\\  z'\\\\  
 \end{array}
 \right) = 0$">|; 

$key = q/displaystyleleft(array{{c}1<row_mark>x<row_mark>y<row_mark>z<row_mark>array{righc}1<row_mark>x'<row_mark>y'<row_mark>z'<row_mark>array{right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="180" HEIGHT="128" ALIGN="MIDDLE" BORDER="0"
 SRC="img13.gif"
 ALT="$\displaystyle \left(
 \begin{array}{c}
 1\\\\  x\\\\  y\\\\  z\\\\  
 \end{array}
 \rig...
...cal{M}} \left(
 \begin{array}{c}
 1\\\\  x'\\\\  y'\\\\  z'\\\\  
 \end{array}
 \right)$">|; 

$key = q/,A^3(K),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="img2.gif"
 ALT="$ \,A^3(K)\,$">|; 

$key = q/,mathcal{Q}=T(mathcal{D});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="img6.gif"
 ALT="$ \,\mathcal{Q} =
T(\mathcal{D})$">|; 

$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="img18.gif"
 ALT="$ \,
\mathcal{B} \,$">|; 

$key = q/,mathcal{M}=(m_{ij})inGL_3(K),,c_1,,c_2,,c_3inK;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="311" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="img8.gif"
 ALT="$ \,\mathcal{M} = (m_{ij}) \in GL_3(K),\,
c_1,\, c_2,\, c_3 \in K$">|; 

$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="img4.gif"
 ALT="$ \,\mathcal{D}\,$">|; 

$key = q/displaystylemathcal{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="137" HEIGHT="46" ALIGN="MIDDLE" BORDER="0"
 SRC="img16.gif"
 ALT="$\displaystyle \mathcal{B}\: = \hspace{2mm}
 ^t\widetilde{\mathcal{M}} \hspace{1mm} \mathcal{A} \hspace{1mm}
 \widetilde{\mathcal{M}}.$">|; 

$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="img7.gif"
 ALT="$ \,\mathcal{Q}$">|; 

$key = q/:mathcal{M},:c_1,c_2,c_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="img11.gif"
 ALT="$ \: \mathcal{M},\:c_1,c_2,c_3$">|; 

$key = q/T;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="img5.gif"
 ALT="$ T$">|; 

$key = q/E^3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="img3.gif"
 ALT="$ E^3$">|; 

$key = q/displaystyleleft{array{{c}x=m_{11}x'+m_{12}y'+m_{13}z'+c_1<row_mark>y=m_{21}x'+mw_mark>z=m_{31}x'+m_{32}y'+m_{33}z'+c_3<row_mark>array{right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="295" HEIGHT="101" ALIGN="MIDDLE" BORDER="0"
 SRC="img9.gif"
 ALT="$\displaystyle \left\{
 \begin{array}{c}
 x = m_{11}x'+m_{12}y'+m_{13}z'+c_1\\\\  ...
...+m_{23}z'+c_2\\\\  
 z = m_{31}x'+m_{32}y'+m_{33}z'+c_3\\\\  
 \end{array}
 \right.$">|; 

$key = q/{displaymath}left(array{{c}x<row_mark>y<row_mark>z<row_mark>array{right)=left(ar<row_mark>c_2<row_mark>c_3<row_mark>array{right){displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="403" HEIGHT="90" BORDER="0"
 SRC="img12.gif"
 ALT="\begin{displaymath}
\left(
\begin{array}{c}
x\\\\  y\\\\  z\\\\
\end{array}
\ri...
...\begin{array}{c}
c_1\\\\  c_2\\\\  c_3\\\\
\end{array}
\right)
\end{displaymath}">|; 

$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/,mathcal{B}_0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="img17.gif"
 ALT="$ \, \mathcal{B}_0 \,$">|; 

1;

