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MathGroup Archive 2001

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Re: diagonalization

  • To: mathgroup at
  • Subject: [mg31349] Re: diagonalization
  • From: Jens-Peer Kuska <kuska at>
  • Date: Tue, 30 Oct 2001 04:35:32 -0500 (EST)
  • Organization: Universitaet Leipzig
  • References: <9rdfmc$7nk$>
  • Sender: owner-wri-mathgroup at

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. 


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 ?


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