       Re: Sorting Eigenvalues/EigenVectors

• To: mathgroup at smc.vnet.net
• Subject: [mg8393] Re: Sorting Eigenvalues/EigenVectors
• From: murray at math.umass.edu (Murray Eisenberg)
• Date: Tue, 26 Aug 1997 20:41:33 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```Colin, perhaps your "yuck" was justified -- but there WAS a typo in my
original posting, shown below.  The phrase "undoubtedly the most
elegant" should have been "undoubtedly NOT [emphasis added] the most

However, the solution seems straightforward enough:  determine the
desired permutation of the eigenvalues -- use any ordering function
you want -- and then index into them and the eigenvectors with that
permutation.  Isn't that the way you would think about it?  (Even if
you can resort to some sort of witchcraft to code it more elegantly or
succinclty.)

Colin Rose (crose at c2.telstra-mm.net.au) wrote:
: murray at math.umass.edu (Murray Eisenberg) wrote:

:
:   > Here's one way -- undoubtedly the most elegant.

:   > a = {{16,19,1},{18,10,20},{10,5,3}};
:   > esys = N[Eigensystem[a]]
:   > evals = esys[]; evect = esys[]
:   > (* Sort[evals] gives the sorted list.  That's not all you want. *)
:   > where = Flatten[Map[Position[Sort[evals], #]&, evals]]
:   > evals[[where]]
:   > evects[[where]]

: Yuck.

: --
: Colin Rose
: tr(I) - Theoretical Research Institute
: ______________________________________
: crose at c2.telstra-mm.net.au
: http://www.usyd.edu.au/su/tri/

--
Murray Eisenberg                       Internet:  murray at math.umass.edu
Mathematics & Statistics Dept.            Voice:  413-545-2859 (W)
University of Massachusetts                       413-549-1020 (H)
Amherst, MA 01003                           Fax:  413-545-1801

```

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