function [] = prob_10_8
% PROB_10_8 - 
% 
% Written by:
% -- 
% John L. Weatherwax                2005-08-28
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

P = gallery( 'pascal', 12 )
F = gallery( 'frank', 12 )

ep = eig( P ); 
ef = eig( F );

[ ep.'; fliplr( ( 1./ep ).' ) ]
disp('')
[ ef.'; fliplr( ( 1./ef ).' ) ]

condeig( P ).'
condeig( F ).'

% Note the eigenvalue condition estimate for the pascal matrix is 
% the ideal value of 1, while the same estimate for the frank 
% matrix is ~10^7.  This explains why so few eigenvalues match
% a reciprical for the frank matrix.