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