- 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: <firstname.lastname@example.org>
- Sender: owner-wri-mathgroup at wolfram.com
I would calculate Det[M- lam IdentityMatrix]; 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
> 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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