# LaTeX2HTML 0.6.4 (Tues Aug 30 1994)
# Associate image original text (scrambled) with physical files.
$key = q/{}$Z${}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}A-muB=PLU{displaymath}/;
$cached_env_img{$key} ='
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$key = q/{}$X${}/;
$cached_env_img{$key} ='
';
$key = q/{}$lambda_n-m+1${}/;
$cached_env_img{$key} ='
';
$key = q/{}$Ap${}/;
$cached_env_img{$key} ='
';
$key = q/{}$T_B${}/;
$cached_env_img{$key} ='
';
$key = q/{}$T${}/;
$cached_env_img{$key} ='
';
$key = q/{}$o(n^2)${}/;
$cached_env_img{$key} ='
';
$key = q/{}$left[arraycc0;html_special_mark_amp;AA^H;html_special_mark_amp;0arrayright]-lambdaleft[arrayccI;html_special_mark_amp;00;html_special_mark_amp;B^HBemat${}/;
$cached_env_img{$key} ='
';
$key = q/{}$r^(i)${}/;
$cached_env_img{$key} ='
';
$key = q/{}$A-lambdaB${}/;
$cached_env_img{$key} ='
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$key = q/{}$A^HA-lambdaB^HB${}/;
$cached_env_img{$key} ='
';
$key = q/{}$S^-1AS${}/;
$cached_env_img{$key} ='
';
$key = q/{}$beta${}/;
$cached_env_img{$key} ='
';
$key = q/{}$L${}/;
$cached_env_img{$key} ='
';
$key = q/{}$mu${}/;
$cached_env_img{$key} ='
';
$key = q/{}$J${}/;
$cached_env_img{$key} ='
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$key = q/{}$epsilon${}/;
$cached_env_img{$key} ='
';
$key = q/{}$kleqn${}/;
$cached_env_img{$key} ='
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$key = q/{}$O(n^3)${}/;
$cached_env_img{$key} ='
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$key = q/{}$A(lambda,mu)${}/;
$cached_env_img{$key} ='
';
$key = q/{}fboxttLevel2ofDecisionTree{}/;
$cached_env_img{$key} ='
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$key = q/{}$D${}/;
$cached_env_img{$key} ='
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$key = q/{}$B${}/;
$cached_env_img{$key} ='
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$key = q/{}$Mz=r${}/;
$cached_env_img{$key} ='
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$key = q/{}$S_L^-1AS_R-lambdaS_L^-1BS_R${}/;
$cached_env_img{$key} ='
';
$key = q/{}$b-Ax^(i)${}/;
$cached_env_img{$key} ='
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$key = q/{tabbing}llaaa=bbb=ccc=kill>bffor$i=1,n$>>$q(i)=0$>>bffor$j=row_ptr(i),row_ptr(i+1)-1$>>>$q(i)=q(i)+val(j)timesp(col_ind(j))$>>bf>bf{tabbing}/;
$cached_env_img{$key} ='
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$key = q/{}$A=QLambdaQ^H${}/;
$cached_env_img{$key} ='
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$key = q/{}$Ax=b${}/;
$cached_env_img{$key} ='
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$key = q/{table}labeltab_selfadjointcentertabular|c||c|c|c|hlineProblemType;html_special_mark_amp;``Schur'';html_special_mark_amp;``Jordan-Schur'';html_special_mark_amp;``Jordan''hlinehline$A-lambdaI$;html_special_mark_amp;$Q^HAQ=Lambda$;html_special_mark_amp;sameasSchur;html_special_mark_amp;sameasSchurhline$A-lambdaB$;html_special_mark_amp;$Q^HAZ=T_A$;html_special_mark_amp;$Q^HAZ=T_S,A$;html_special_mark_amp;$S^HAS=Lambda_A$;html_special_mark_amp;$Q^HBZ=T_B$;html_special_mark_amp;$Q^HBZ=T_S,B$;html_special_mark_amp;$S^HBS=Lambda_B$hlineSVDof$A$;html_special_mark_amp;$Q^HAZ=Sigma$;html_special_mark_amp;sameasSchur;html_special_mark_amp;sameasSchurhlineQSVDof$A$,$B$;html_special_mark_amp;$Q^HAS=Sigma_A$;html_special_mark_amp;sameasSchur;html_special_mark_amp;sameasSchur;html_special_mark_amp;$Z^HBS=Sigma_B$;html_special_mark_amp;sameasSchur;html_special_mark_amp;sameasSchurhlinetabularcenter{table}/;
$cached_env_img{$key} ='
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$key = q/{}$Sigma_A${}/;
$cached_env_img{$key} ='
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$key = q/{}$y${}/;
$cached_env_img{$key} ='
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$key = q/{}$k=n${}/;
$cached_env_img{$key} ='
';
$key = q/{}$O(n^2)${}/;
$cached_env_img{$key} ='
';
$key = q/{}$y=(A-muB)^-1Bx${}/;
$cached_env_img{$key} ='
';
$key = q/{}$XBX^H=Lambda_B${}/;
$cached_env_img{$key} ='
';
$key = q/{}$y=B^H(A-muB)^-Hx${}/;
$cached_env_img{$key} ='
';
$key = q/{}$T_S${}/;
$cached_env_img{$key} ='
';
$key = q/{}$tau${}/;
$cached_env_img{$key} ='
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$key = q/{}$D_C${}/;
$cached_env_img{$key} ='
';
$key = q/{}$m${}/;
$cached_env_img{$key} ='
';
$key = q/{}$lambda^2A+lambdaB+C${}/;
$cached_env_img{$key} ='
';
$key = q/{}$k${}/;
$cached_env_img{$key} ='
';
$key = q/{}$B=B^H${}/;
$cached_env_img{$key} ='
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$key = q/{}$A^Tp${}/;
$cached_env_img{$key} ='
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$key = q/{}$k;html_special_mark_lt;n${}/;
$cached_env_img{$key} ='
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$key = q/{}fboxttLevel1ofDecisionTree{}/;
$cached_env_img{$key} ='
';
$key = q/{}$|A|${}/;
$cached_env_img{$key} ='
';
$key = q/{}$A-lambdaI${}/;
$cached_env_img{$key} ='
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$key = q/{}$A^H=-A${}/;
$cached_env_img{$key} ='
';
$key = q/{}$AA^H-lambdaBB^H${}/;
$cached_env_img{$key} ='
';
$key = q/{}$det(A-lambdaB)${}/;
$cached_env_img{$key} ='
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$key = q/{}$A^HA${}/;
$cached_env_img{$key} ='
';
$key = q/{}$lambda_1${}/;
$cached_env_img{$key} ='
';
$key = q/{}$y=(A-muI)^-Hx${}/;
$cached_env_img{$key} ='
';
$key = q/{}$y=A^Hx${}/;
$cached_env_img{$key} ='
';
$key = q/{}$(A-lambdaB)x=0${}/;
$cached_env_img{$key} ='
';
$key = q/{}$U${}/;
$cached_env_img{$key} ='
';
$key = q/{}$B=I${}/;
$cached_env_img{$key} ='
';
$key = q/{}$S${}/;
$cached_env_img{$key} ='
';
$key = q/{}$Sigma_B${}/;
$cached_env_img{$key} ='
';
$key = q/{}$Q${}/;
$cached_env_img{$key} ='
';
$key = q/{}$A-muI${}/;
$cached_env_img{$key} ='
';
$key = q/{}$M${}/;
$cached_env_img{$key} ='
';
$key = q/{}$A^H${}/;
$cached_env_img{$key} ='
';
$key = q/{}$T_S_B${}/;
$cached_env_img{$key} ='
';
$key = q/{}$(A-muI)^-1${}/;
$cached_env_img{$key} ='
';
$key = q/{}$|A-B|leqepsilon${}/;
$cached_env_img{$key} ='
';
$key = q/{}$x_i${}/;
$cached_env_img{$key} ='
';
$key = q/{}$K${}/;
$cached_env_img{$key} ='
';
$key = q/{}$exp(A)x${}/;
$cached_env_img{$key} ='
';
$key = q/{}$XAX^H=Lambda_A${}/;
$cached_env_img{$key} ='
';
$key = q/{}$B=B^H;html_special_mark_gt;0${}/;
$cached_env_img{$key} ='
';
$key = q/{}$U_S${}/;
$cached_env_img{$key} ='
';
$key = q/{}$tau;html_special_mark_gt;0${}/;
$cached_env_img{$key} ='
';
$key = q/{}$lambda${}/;
$cached_env_img{$key} ='
';
$key = q/{}$iincalI${}/;
$cached_env_img{$key} ='
';
$key = q/{}$S_L${}/;
$cached_env_img{$key} ='
';
$key = q/{}$Sigmalambda^iA_i${}/;
$cached_env_img{$key} ='
';
$key = q/{}$y=Ax${}/;
$cached_env_img{$key} ='
';
$key = q/{}$C${}/;
$cached_env_img{$key} ='
';
$key = q/{}$Sigma${}/;
$cached_env_img{$key} ='
';
$key = q/{}$O(n)${}/;
$cached_env_img{$key} ='
';
$key = q/{}$M=(L+D_C)D_C^-1(D_C+L^T)${}/;
$cached_env_img{$key} ='
';
$key = q/{}$sqrt-1${}/;
$cached_env_img{$key} ='
';
$key = q/{}$A${}/;
$cached_env_img{$key} ='
';
$key = q/{}$muA-B${}/;
$cached_env_img{$key} ='
';
$key = q/{}fboxttLevel4ofDecisionTree{}/;
$cached_env_img{$key} ='
';
$key = q/{}$lambda_1leqlambda_2leqcdotsleqlambda_n${}/;
$cached_env_img{$key} ='
';
$key = q/{}$x^(i)${}/;
$cached_env_img{$key} ='
';
$key = q/{}$x${}/;
$cached_env_img{$key} ='
';
$key = q/{}$left[arraycc0;html_special_mark_amp;AA^H;html_special_mark_amp;0emat${}/;
$cached_env_img{$key} ='
';
$key = q/{}$A=BB^H${}/;
$cached_env_img{$key} ='
';
$key = q/{}$n=25${}/;
$cached_env_img{$key} ='
';
$key = q/{}$|A^-1|${}/;
$cached_env_img{$key} ='
';
$key = q/{}$3${}/;
$cached_env_img{$key} ='
';
$key = q/{}$mu_i=0${}/;
$cached_env_img{$key} ='
';
$key = q/{displaymath}Ax_i=lambda_iBx_i;;;;;y_i^HA=lambda_iy_i^HB,{displaymath}/;
$cached_env_img{$key} ='
';
$key = q/{}$(A-muB)x=b${}/;
$cached_env_img{$key} ='
';
$key = q/{}$r${}/;
$cached_env_img{$key} ='
';
$key = q/{}$p${}/;
$cached_env_img{$key} ='
';
$key = q/{}$T_A${}/;
$cached_env_img{$key} ='
';
$key = q/{}$Lambda_A${}/;
$cached_env_img{$key} ='
';
$key = q/{}$S_R${}/;
$cached_env_img{$key} ='
';
$key = q/{}$n${}/;
$cached_env_img{$key} ='
';
$key = q/{}$Lambda_B${}/;
$cached_env_img{$key} ='
';
$key = q/{table}labeltab_nonselfadjointcentertabular|c||c|c|c|hlineProblemType;html_special_mark_amp;``Schur'';html_special_mark_amp;``Jordan-Schur'';html_special_mark_amp;``Jordan''hlinehline$A-lambdaI$;html_special_mark_amp;$Q^HAQ=T$;html_special_mark_amp;$Q^HAQ=T_S$;html_special_mark_amp;$S^-1AS=J$hline$A-lambdaB$,regular;html_special_mark_amp;$Q^HAZ=T_A$;html_special_mark_amp;$Q^HAZ=T_S,A$;html_special_mark_amp;$S_L^-1AS_R=J_A$;html_special_mark_amp;$Q^HBZ=T_B$;html_special_mark_amp;$Q^HBZ=T_S,B$;html_special_mark_amp;$S_L^-1BS_R=J_B$hline$A-lambdaB$,singular;html_special_mark_amp;$Q^HAZ=U_A$;html_special_mark_amp;$Q^HAZ=U_S,A$;html_special_mark_amp;$S_L^-1AS_R=K_A$;html_special_mark_amp;$Q^HBZ=U_B$;html_special_mark_amp;$Q^HBZ=U_S,B$;html_special_mark_amp;$S_L^-1BS_R=K_B$hlinetabularcenter{table}/;
$cached_env_img{$key} ='
';
$key = q/{}$A=L+D+L^T${}/;
$cached_env_img{$key} ='
';
$key = q/{}$A=BC^-1${}/;
$cached_env_img{$key} ='
';
$key = q/{}$A=A^H${}/;
$cached_env_img{$key} ='
';
$key = q/{}$T_S,A${}/;
$cached_env_img{$key} ='
';
$key = q/{}$lambda_i${}/;
$cached_env_img{$key} ='
';
$key = q/{}$y=(A-muI)^-1x${}/;
$cached_env_img{$key} ='
';
$key = q/{}$Lambda${}/;
$cached_env_img{$key} ='
';
$key = q/{}$lambda_1leqlambda_2leqcdotsleqlambda_k${}/;
$cached_env_img{$key} ='
';
$key = q/{}$y_i${}/;
$cached_env_img{$key} ='
';
$key = q/{}$lambda_m${}/;
$cached_env_img{$key} ='
';
$key = q/{}$AB^-1${}/;
$cached_env_img{$key} ='
';
$key = q/{}$lambda_n${}/;
$cached_env_img{$key} ='
';
$key = q/{}$Q^HAQ=Lambda${}/;
$cached_env_img{$key} ='
';
$key = q/{}$exp(A)${}/;
$cached_env_img{$key} ='
';
$key = q/{}$A(lambda)${}/;
$cached_env_img{$key} ='
';
$key = q/{}$A^T${}/;
$cached_env_img{$key} ='
';
$key = q/{}fboxttLevel3ofDecisionTree{}/;
$cached_env_img{$key} ='
';
$key = q/{}$lambda_1,...,lambda_k${}/;
$cached_env_img{$key} ='
';
$key = q/{}$n=100${}/;
$cached_env_img{$key} ='
';
1;