
From:  Patrick Alken 
Subject:  Re: [Buggsl] Re: [Helpgsl] error in Schur decomposition of a nonsymmetric matrix ? 
Date:  Tue, 23 Mar 2010 09:28:33 0600 
Useragent:  Mozilla/5.0 (X11; U; Linux i686 (x86_64); enUS; rv:1.9.1.8) Gecko/20100227 Thunderbird/3.0.3 
The rest of A (below the subdiagonal) is not guaranteed to be 0, as far as I remember.
It just occurred to me, that the rest of A below the subdiagonal is probably very close to 0, ie to machine precision due to the way the eigenvalue decomposition algorithm works, however at no point are these values set identically to 0.0, whereas the subdiagonal elements are set to 0.0 in the case of real eigenvalues (this is done to help the eigenvector solver detect whether or not they are real or complex eigenvalues).
So the bottom of A may contain values like 2.3e15 or somesuch. The function gsl_linalg_hessenberg_set_zero will set these values identically to 0.0 if thats what you want.
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