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Re: What's up with the order of Eigenvalues

  • To: mathgroup at smc.vnet.net
  • Subject: [mg105811] Re: What's up with the order of Eigenvalues
  • From: Bill Rowe <readnews at sbcglobal.net>
  • Date: Sun, 20 Dec 2009 06:53:34 -0500 (EST)

On 12/19/09 at 6:24 AM, alexandrepassosalmeida at gmail.com (mokambo)
wrote:


>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[]?

Per the documentation, Eigenvalues returns eigenvalues with
numeric values in order of decreasing absolute value. That is:

In[2]:= OrderedQ[Reverse@Abs[Eigenvalues[m]] // N]

Out[2]= True



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