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>
- What's up with the order of Eigenvalues