# LaTeX2HTML 2019.2 (Released June 5, 2019)
# Associate images original text with physical files.


$key = q/alpha;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.19ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img5.svg"
 ALT="$\alpha$">|; 

$key = q/alpha{svectorm}_1+beta{svectorm}_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.25ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img7.svg"
 ALT="$\alpha
{\svector m}_1 + \beta {\svector m}_2$">|; 

$key = q/beta;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.25ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img6.svg"
 ALT="$\beta$">|; 

$key = q/displaystyle+({svectorm_0}+alpha{svectorDelta{svectorm}})cdot{{stensorC}}_m^{-1}cdot({svectorm_0}+alpha{svectorDelta{svectorm}}).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.74ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img28.svg"
 ALT="$\displaystyle + ({\svector m_0}+ \alpha {\svector \Delta {\svector m}}) \cdot {{\stensor C}}_m^{-1}\cdot ({\svector m_0}+ \alpha {\svector \Delta {\svector m}}).$">|; 

$key = q/displaystyle+({svectorm_0}+{svectorDelta{svectorm}})cdot{{stensorC}}_m^{-1}cdot({svectorm_0}+{svectorDelta{svectorm}}).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.74ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img25.svg"
 ALT="$\displaystyle + ({\svector m_0}+ {\svector \Delta {\svector m}}) \cdot {{\stensor C}}_m^{-1}\cdot ({\svector m_0}+ {\svector \Delta {\svector m}}).$">|; 

$key = q/displaystylemin_{alpha}~[{svectord}-{svectorf}({svectorm_0}+alpha{svectorDelta{stord}-{svectorf}({svectorm_0}+alpha{svectorDelta{svectorm}})];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 3.51ex; vertical-align: -1.45ex; " SRC="|."$dir".q|img27.svg"
 ALT="$\displaystyle \min_{\alpha}&nbsp; [{\svector d}- {\svector f}({\svector m_0}+ \alph...
...ector d}- {\svector f}({\svector m_0}+ \alpha {\svector \Delta {\svector m}}) ]$">|; 

$key = q/displaystylemin_{{svectorDelta{svectorm}}}~[{svectord}-{svectorf}({svectorm_0})-m_0})-{{stensorF}({svectorm_0})}cdot{svectorDelta{svectorm}}];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 4.27ex; vertical-align: -2.21ex; " SRC="|."$dir".q|img24.svg"
 ALT="$\displaystyle \min_{{\svector \Delta {\svector m}}}&nbsp; [{\svector d}- {\svector ...
...or m_0}) - {{\stensor F}( {\svector m_0})}\cdot {\svector \Delta {\svector m}}]$">|; 

$key = q/displaystylemin_{{svectorm}}~{[{svectord}-{svectorf}({svectorm})]cdot{{stensorC}svectorm})]+{svectorm}cdot{{stensorC}}_m^{-1}cdot{svectorm}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 3.71ex; vertical-align: -1.65ex; " SRC="|."$dir".q|img23.svg"
 ALT="$\displaystyle
\min_{{\svector m}}&nbsp; \{ [{\svector d}- {\svector f}({\svector m}...
...svector m}) ]
+ {\svector m}\cdot {{\stensor C}}_m^{-1}\cdot {\svector m}\} .
$">|; 

$key = q/displaystyle{stensorG}({svectorm_0})approx[{{stensorF}^T({svectorm_0})}cdot{{stensorF}({svectorm_0})}]^{-1},~mbox{or};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.80ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img32.svg"
 ALT="$\displaystyle {\stensor G}( {\svector m_0}) \approx [ {{\stensor F}^T ( {\svector m_0})}\cdot {{\stensor F}( {\svector m_0})}]^{-1},&nbsp; \mbox{or}$">|; 

$key = q/displaystyle{stensorG}({svectorm_0})cdot[{{stensorF}^T({svectorm_0})}cdot{{stensorF}({svectorm_0})}]approx{{stensorI}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.80ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img33.svg"
 ALT="$\displaystyle {\stensor G}( {\svector m_0}) \cdot [ {{\stensor F}^T ( {\svector m_0})}\cdot {{\stensor F}( {\svector m_0})}] \approx {{\stensor I}}.$">|; 

$key = q/displaystyle{svectorDelta{svectord}}={{stensorF}({svectorm_0})}cdot{svectorDeltaectorm_0}+{svectorDelta{svectorm}})-{svectorf}({svectorm_0}).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img15.svg"
 ALT="$\displaystyle {\svector \Delta {\svector d}}= {{\stensor F}( {\svector m_0})}\c...
...ector m_0}+ {\svector \Delta {\svector m}}) - {\svector f}( {\svector m_0}) .
$">|; 

$key = q/displaystyle{svectorDelta{svectord}}cdot[{{stensorF}({svectorm_0})}cdot{svectorD~{svectorDelta{svectord}}~mbox{and}~{svectorDelta{svectorm}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.80ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img19.svg"
 ALT="$\displaystyle {\svector \Delta {\svector d}}\cdot [ {{\stensor F}( {\svector m_...
...&nbsp;{\svector \Delta {\svector d}}&nbsp;
\mbox{and}&nbsp;{\svector \Delta {\svector m}}.
$">|; 

$key = q/displaystyle{svectord}={svectorf}({svectorm})+{svectorn}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img22.svg"
 ALT="$\displaystyle {\svector d}= {\svector f}( {\svector m}) + {\svector n}.
$">|; 

$key = q/displaystyle{{stensorF}({svectorm_0})}cdot(alpha{svectorDelta{svectorm}}_1+beta{beta~{{stensorF}({svectorm_0})}cdot{svectorDelta{svectorm}}_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img16.svg"
 ALT="$\displaystyle {{\stensor F}( {\svector m_0})}\cdot (\alpha {\svector \Delta {\s...
...+ \beta&nbsp; {{\stensor F}( {\svector m_0})}\cdot {\svector \Delta {\svector m}}_2$">|; 

$key = q/displaystyle~mbox{forall}~alpha,beta,{svectorDelta{svectorm}}_1,~mbox{and}~{svectorDelta{svectorm}}_2.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.25ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img17.svg"
 ALT="$\displaystyle&nbsp;\mbox{for all}&nbsp; \alpha, \beta, {\svector \Delta {\svector m}}_1,&nbsp;\mbox{and}&nbsp; {\svector \Delta {\svector m}}_2 .$">|; 

$key = q/{stensorF}^T({svectorm_0});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.80ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img18.svg"
 ALT="${\stensor F}^T
({\svector m_0})$">|; 

$key = q/{stensorG}({svectorm_0});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img31.svg"
 ALT="${\stensor G}( {\svector m_0})$">|; 

$key = q/{stensorG}cdot{stensorF}^Tcdot{stensorF};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.67ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img34.svg"
 ALT="${\stensor G}\cdot
{\stensor F}^T \cdot {\stensor F}$">|; 

$key = q/{stensorP};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.23ex; vertical-align: -0.55ex; " SRC="|."$dir".q|img30.svg"
 ALT="${\stensor P}$">|; 

$key = q/{stensorP}cdot{svectord}={stensorP}cdot{svectorf}({svectorm});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img29.svg"
 ALT="${\stensor P}\cdot {\svector d}= {\stensor P}\cdot {\svector f}({\svector m})$">|; 

$key = q/{svectorDelta{svectord}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.80ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img13.svg"
 ALT="${\svector \Delta {\svector d}}$">|; 

$key = q/{svectorDelta{svectorm}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.78ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img11.svg"
 ALT="${\svector \Delta {\svector m}}$">|; 

$key = q/{svectord}-{svectorf}({svectorm_0});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img26.svg"
 ALT="${\svector d}- {\svector f}({\svector m_0})$">|; 

$key = q/{svectord};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.80ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img1.svg"
 ALT="${\svector d}$">|; 

$key = q/{svectord}={svectorf}({svectorm});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img10.svg"
 ALT="${\svector d}= {\svector f}( {\svector m})$">|; 

$key = q/{svectorf}({svectorm});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img20.svg"
 ALT="${\svector f}({\svector m})$">|; 

$key = q/{svectorm_0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.57ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img12.svg"
 ALT="${\svector m_0}$">|; 

$key = q/{svectorm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.22ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img2.svg"
 ALT="${\svector m}$">|; 

$key = q/{svectorm}_1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.57ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img3.svg"
 ALT="${\svector m}_1$">|; 

$key = q/{svectorm}_1cdot{svectorm}_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.57ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img8.svg"
 ALT="${\svector m}_1 \cdot {\svector m}_2$">|; 

$key = q/{svectorm}_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.57ex; vertical-align: -0.45ex; " SRC="|."$dir".q|img4.svg"
 ALT="${\svector m}_2$">|; 

$key = q/{svectorn};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 1.22ex; vertical-align: -0.10ex; " SRC="|."$dir".q|img21.svg"
 ALT="${\svector n}$">|; 

$key = q/{{stensorF}({svectorm_0})};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.51ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img14.svg"
 ALT="${{\stensor F}( {\svector m_0})}$">|; 

$key = q/|{svectorm}|^2equiv{svectorm}cdot{{stensorC}}_m^{-1}cdot{svectorm};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG STYLE="height: 2.74ex; vertical-align: -0.68ex; " SRC="|."$dir".q|img9.svg"
 ALT="$\Vert
{\svector m}\Vert^2 \equiv {\svector m}\cdot {{\stensor C}}_m^{-1}\cdot {\svector m}$">|; 

1;

