Eigensystem ordering
- To: mathgroup at yoda.physics.unc.edu (Mathematica User's Group)
- Subject: Eigensystem ordering
- From: Keith Clay <clay at galileo.phys.washington.edu>
- Date: Tue, 21 Sep 93 9:27:57 MDT
The following question came to me from two fellow Mathematica users,
and I cannot find an answer in any of the standard literature:
> When you call Eigensystem[m], you get a result of the form:
>
> { n-vector, {vector1, vector2, ... , vector_n}}
>
> Q: Does the ith Eigenvalue in n-vector ALWAYS correspond to the ith
> Eigenvector in the list? It usually does, but we want to know if this
> can always be assumed. ONE OF US THINKS THIS SHOULD BE TRUE, ANOTHER
> THINKS THEY HAVE SEEN A CASE TO THE CONTRARY.
In other words, can we be sure this quantity is always zero
Eigensystem[m][[1,i]]*Eigensystem[m][[2,i]] - m.Eigensystem[m][[2,i]]
(with the same i used for the eigenvector and eigenvalue)?
Has anyone else seen a case to the contrary?
(Page 664 of The Book says that this is true for one matrix, for i=1.
Searching for exceptions has turned up none, but these people are looking
for certainty.)
It would certainly seem absurd to report the results any other way, but
I can't find any guarantees or details of how the output is put together.
Thanks.
------------------------------------------------------------------------
Keith Clay Department of Physics, FM-15
(clay at galileo.phys.washington.edu) University of Washington
( -or- clay at phys.washington.edu ) Seattle, WA 98195