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MathGroup Archive 1998

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Re: Eigenvalue

  • To: mathgroup at smc.vnet.net
  • Subject: [mg14190] Re: Eigenvalue
  • From: Alan Lewis <alan at enfs.com>
  • Date: Wed, 30 Sep 1998 19:42:23 -0400
  • Organization: @Home Network
  • References: <6ush0k$5k7@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi Ferrucio,

     I would calculate Det[M- lam IdentityMatrix[9]]; then do a Series
of this about s=0 and and g=0. Now you want answers of the form lam =
lam(0) + s lam(1) + g lam(2) + .... If you substitute this in, then the
constant term and each of the coefs of s,s^2,g,g^2, and sg should be
separately zero. The resulting 6 eqns can likely be solved by
Mathematica.

Alan

RENZONI_FERRUCCIO wrote:
> 
> Dear MathUsers,
> 
> I have a 9x9 real matrix M containing 3 parameters (say, s, g and b).
> 
> I would like to find an analytic expression for the eigenvalues of M at
> the second order in the parameters s and g (the expansion is around s=0
> and g=0). I tought to find the eigenvalue as Root objects and then to
> expand them in Taylor series. For some eigenvalue works fine, for some
> other not. I obviously verified numerically that all the eigenvalues
> exist and are finite.
> 
> Are there other way to find eigenvalues at a given order in the
> parameters without using Root object?
> 
> E-mail to me directly please.
> 
> Thanks a lot,
> 
> Ferruccio Renzoni


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