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Re: What's up with the order of Eigenvalues

  • To: mathgroup at smc.vnet.net
  • Subject: [mg105825] Re: [mg105786] What's up with the order of Eigenvalues
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Sun, 20 Dec 2009 06:56:30 -0500 (EST)
  • Reply-to: hanlonr at cox.net

According to the Eigenvalues documentation:

"If they are numeric, eigenvalues are sorted in order of decreasing absolute value."

It did what it said that it would do.


Bob Hanlon

---- mokambo <alexandrepassosalmeida at gmail.com> 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[]?


--

Bob Hanlon



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