Path: news.mathworks.com!not-for-mail From: <HIDDEN> Newsgroups: comp.soft-sys.matlab Subject: Re: Finding the nearest matrix with real eigenvalues Date: Wed, 1 Sep 2010 14:12:20 +0000 (UTC) Organization: The MathWorks, Inc. Lines: 9 Message-ID: <i5ln03$lje$1@fred.mathworks.com> References: <i5j67v$4s4$1@fred.mathworks.com> <i5jicf$29u$1@fred.mathworks.com> <i5jn7k$pdd$1@fred.mathworks.com> <i5jvad$c2b$1@fred.mathworks.com> Reply-To: <HIDDEN> NNTP-Posting-Host: webapp-05-blr.mathworks.com Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit X-Trace: fred.mathworks.com 1283350340 22126 172.30.248.35 (1 Sep 2010 14:12:20 GMT) X-Complaints-To: news@mathworks.com NNTP-Posting-Date: Wed, 1 Sep 2010 14:12:20 +0000 (UTC) X-Newsreader: MATLAB Central Newsreader 1187260 Xref: news.mathworks.com comp.soft-sys.matlab:666848 "Roger Stafford" <ellieandrogerxyzzy@mindspring.com.invalid> wrote in message <i5jvad$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