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What's up with the order of Eigenvalues

• To: mathgroup at smc.vnet.net
• Subject: [mg105786] What's up with the order of Eigenvalues
• From: mokambo <alexandrepassosalmeida at gmail.com>
• Date: Sat, 19 Dec 2009 06:24:50 -0500 (EST)

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[]?

• Follow-Ups:
  • Re: What's up with the order of Eigenvalues
    • From: Murray Eisenberg <murray@math.umass.edu>