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