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Subject: Re: Finding the nearest matrix with real eigenvalues
Date: Wed, 1 Sep 2010 14:12:20 +0000 (UTC)
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"Roger Stafford" <ellieandrogerxyzzy@mindspring.com.invalid> wrote in message <i5jvad$c2b$1@fred.mathworks.com>...
> > >  [V,D] = eig(A);
> > >  A1 = real(V*real(D)/V);
> > > .......
>   ....  The only thing I can prove offhand is the claim I made that with small imaginary parts in the original eigenvalues, you get A1 close to A in the sense that the determinant of their difference is small. .....
- - - - - - - - - -
  The argument I made yesterday was faulty.  Having a matrix with a small determinant does not mean its elements are small.  However, in the experiments I ran generating random 3 x 3 matrices with small imaginary components in their eigenvalues, the changes made when these were removed were always correspondingly small.  So at this point I have only an empirical justification for the procedure I gave.

Roger Stafford