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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