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Re: What's up with the order of Eigenvalues

• To: mathgroup at smc.vnet.net
• Subject: [mg105808] Re: [mg105786] What's up with the order of Eigenvalues
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Sun, 20 Dec 2009 06:53:00 -0500 (EST)
• Organization: Mathematics & Statistics, Univ. of Mass./Amherst
• References: <200912191124.GAA24493@smc.vnet.net>
• Reply-to: murray at math.umass.edu

All that the documentation about Eigenvalues specifies that the result 
is sorted by absolute value (i.e., modulus).

As -1+I and -1-I have the same modulus, that specification does not say 
which would come first.

mokambo wrote:
> Dear all,
> 
> Consider a circulant matrix,
> 
> m = {{0, 1, 1, 0}, {0, 0, 1, 1}, {1, 0, 0, 1}, {1, 1, 0, 0}}
> 
> The eigenvalues of m are:
> 
> Eigenvalues[m]
> 
> = {2, -1 + I, -1 - I, 0}
> 
> But they should be equal to the Discrete Fourier Transform of the
> first row of m
> 
> Fourier[{0, 1, 1, 0}, FourierParameters -> {1, -1}]
> 
> = {2 + 0.I,   -1 - 1.I,   0 + 0.I,   -1. + 1. I}
> 
> So what's up with the order of values given by Eigenvalues[]?
> 

-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305

• References:
  • What's up with the order of Eigenvalues
    • From: mokambo <alexandrepassosalmeida@gmail.com>