options=[1,1e-6,1e-6,1e-6,0];
L0=[ -0.132 -0.882 1.576 0.026 0.681 -0.026 ...
      0.524 0.420 -2.827 0.021 -0.013 0.860]';
[L] = fsolve('fun',L0,options)

% L =
%    -0.1343   -0.6996    1.5995   -0.0358    0.5640   -0.0202
%     0.5262    0.3643   -2.9330    0.0447    0.1168    0.8563
% >> [v,d]=eig(A-B*L) + normalisation
% v =
%   Columns 1 through 4 
%   -0.0877            -0.5304             1.0000             0.0000 - 0.0000i
%    0.0878             0.0219             0.0010            15.5640 + 1.0000i
%    0.0039             0.0028            -0.0041             1.0000 + 6.1585i
%    0.0043             0.0521            -0.2500            -0.0000 + 0.0000i
%    0.9834            -0.0748             0.1402             7.8808 - 9.5021i
%    0.1319             0.8426            -0.5687            -0.1034 +14.5626i
%   Columns 5 through 6 
%    0.0000 - 0.0000i  -0.0500          
%   -0.2794 - 0.5460i  -0.0372          
%   -0.2379 + 0.0602i  -0.0000          
%    0.0000 + 0.0000i   1.0000          
%    0.2197 - 0.4329i   0.0028          
%   -0.5239 + 0.2314i  -0.0038          
% >> d
% d =
%   Columns 1 through 4 
%  -20.3401                  0                  0                  0          
%         0           -10.1700                  0                  0          
%         0                  0            -4.0000                  0          
%         0                  0                  0            -0.6300 + 2.4200i
%         0                  0                  0                  0          
%         0                  0                  0                  0          
%   Columns 5 through 6 
%         0                  0          
%         0                  0          
%         0                  0          
%         0                  0          
%   -0.6300 - 2.4200i        0          
%         0            -0.0500   
% 
% ---
% 
% function f = fun(x)
% 
% L = [x(1:6)' ; x(7:12)'];
% A = [-0.746 0.387 -12.9 0 0.952 6.05;
%       0.024 -0.174 4.31 0 -1.76 -0.416;
%      0.006 -0.999 -0.0578 -0.0369 0.0092 -0.0012; 
%   1 0 0 0 0 0 ;
%   0 0 0 0 -10 0 ; 
% 0 0 0 0 0 -5];
% B=[0 0 ; 0 0 ; 0 0 ; 0 0 ; 20 0 ; 0 10];
% 
% [v,d]=eig(A-B*L);
% [y,ind]=sort(real(diag(d)));
% v = v(:,ind);
% d = d(ind,ind);
% z = [imag(v(2,4)) real(v(2,4)); real(v(3,4)) -imag(v(3,4))]\[1 ; 1];
% z = z(1)+i*z(2);
% 
% v(:,3)=v(:,3)./v(1,3);
% v(:,4)=v(:,4)*z;
% v(:,6)=v(:,6)./v(4,6);
% 
%    
% f = [v(2,3) ; v(3,3); real(v(1,4)); imag(v(1,4)); real(v(4,4)); 
% imag(v(4,4)); real(v(3,6)); d(3,3)+4; real(d(4,4))+0.63; imag(d(4,4))-2.42; 
% d(6,6)+0.05; d(1,1)/d(2,2)-2];
% 
% 
