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MathGroup Archive 1993

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Re: Eigensystem Misbehavior

  • To: mathgroup at yoda.physics.unc.edu
  • Subject: Re: Eigensystem Misbehavior
  • From: Mark E. Kotanchek <mek at guinan.psu.edu>
  • Date: Fri, 8 Oct 93 14:12:40 -0400

Howdy,

I've figured out the problem with Mma's Eigensystem routine! It returns a list  
of the eigenvectors--which in Mma is equivalent to a matrix. However, this list  
of lists is the TRANSPOSE of V in the definition: 


   However, since the eigenvalues are defined as solving R.V =
   V.A, this should imply that A = V'.R.V where the apostrophe
   denotes the Hermitian transpose. (Since V'.V = V.V' = I where I
   is the identity matrix.)
   

Thus, to get back to the diagonal matrix of eigenvalues, I should use 


   Conjugate[V].R.Transpose[V] //Chop // MatrixForm
   


rather than,

   In[76]:=
      Conjugate[Transpose[V]].R.V //Chop // MatrixForm
   

IMHO, the documentation which could have helped me out on this one is a little  
on the sparse side. However, at the moment it appears that the eigensystem  
routine is working -- although, Jesus Rivero may disagree with me.

Thanks for your time and patience,

Mark.
---
Mark Kotanchek
Guidance & Control Dept - 363 ASB
Applied Research Lab/Penn State
P.O. Box 30
State College, PA 16804

e-mail:	mek at guinan.psu.edu (NeXTmail)
TEL:	(814)863-0682
FAX:	(814)863-7843





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