Re: diagonalization

*To*: mathgroup at smc.vnet.net*Subject*: [mg31349] Re: diagonalization*From*: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>*Date*: Tue, 30 Oct 2001 04:35:32 -0500 (EST)*Organization*: Universitaet Leipzig*References*: <9rdfmc$7nk$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Mitsuhiro Arikawa wrote: > > Hello, > > I have one question about "diagonalization". > > There is a case which the eigenvectors are not orthogonal in helmite matrix > diagonalization. In principle the eigenvectors in hermite matrix should be > orthogonal. Such a case may occur in the case there is degeneracy. > > The below program is the example. To make a hermite matrix needs a long > procedure.(Now this is not so important.) Anyway this procedure makes a > hermite matrix "h", which depends on real number "t" and "alpha". > (In this exapmle, I will fix "t=1" and "alpha=0.2") > This program check hermite property and shows the inner product of the > eigenvectors. It should be unit matrix but result by mathematica is not. > > I would like to know how to solve this problem and > the function "Eigensystem" is too blackbox (I do not know what happens in > the calculation). I does what EISPACK does in this case. If you wish orthogonal vectors for degenerated eigenvalues you have to do it by your self. LinearAlgebra`Orthogonalization` may help. But it is up to you to choose a linear combination, that satisfy additional contrains. > I want to know how to control the accuracy. As far as I > know, there is no option on that. Set the precision of the input matrix correct and specify a ZeroTest to be as accurate a possible ? Regards Jens