Re: Eigensystem[hermitianMatrix] sometimes returns

*To*: mathgroup at smc.vnet.net*Subject*: [mg96857] Re: [mg96805] Eigensystem[hermitianMatrix] sometimes returns*From*: DrMajorBob <btreat1 at austin.rr.com>*Date*: Thu, 26 Feb 2009 07:55:56 -0500 (EST)*References*: <200902250904.EAA15732@smc.vnet.net>*Reply-to*: drmajorbob at bigfoot.com

I suppose the simplest thing is Normalize/@Eigenvalues[m] or {First@#,Normalize/@Last@#}&@Eigensystem[m] Bobby On Wed, 25 Feb 2009 03:04:51 -0600, Yen Lee Loh <yloh at mps.ohio-state.edu> wrote: > Dear Mathematica users, > > In Mathematica 7.0.0 (for Linux), calling Eigenvectors[H] or > Eigensystem[H] > for a numerical Hermitian matrix H sometimes returns eigenvectors that > are > not orthonormal. > This happens when some eigenvalues are degenerate. (I can supply example > code that illustrates the problem, if necessary.) > > This is not really a bug -- the documentation for Eigensystem[] doesn't > make > any guarantees of orthonormality -- but nevertheless it is an annoying > part > of Mathematica's design. > This issue has been raised 11 years ago ( > http://forums.wolfram.com/mathgroup/archive/1998/Mar/msg00418.html ), but > that post is corrupted! (Surely Wolfram isn't resorting to > censorship?) I > was hoping that in Mathematica 7 I would be able to write something like > > Eigensystem[H, Method->"LAPACK-ZHEEVR"] > > or > > Eigensystem[H, OrthonormalizeEigenvectors->True] > > but no such options seem to exist. One workaround is to apply > Orthogonalize[] to the matrix of eigenvectors, but the documentation for > Orthogonalize[] doesn't guarantee that the orthonormalization will only > occur within the "degenerate subspace". So one has to resort to > complicated > fixes (e.g., http://arxiv.org/pdf/hep-ph/9607313 ). > Does anyone have a simpler solution? (For example, is there an easy way > to > call LAPACK'S ZHEEVR routine, which guarantees orthornormal eigenvectors, > from Mathematica?) > > Thanks a lot. > Yen Lee Loh > > -- DrMajorBob at longhorns.com

**References**:**Eigensystem[hermitianMatrix] sometimes returns non-orthonormal***From:*Yen Lee Loh <yloh@mps.ohio-state.edu>