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Determining the root of the characteristic equation for time series model

• To: mathgroup at smc.vnet.net
• Subject: [mg113442] Determining the root of the characteristic equation for time series model
• From: Christofer Bogaso <bogaso.christofer at gmail.com>
• Date: Fri, 29 Oct 2010 06:26:39 -0400 (EDT)

Hello all,

I am a new user of Mathematica and would appreciate if somebody help
me with some hints how can I use Mathematica to solve a typical
problem.

Suppose I have a matrix polynomial for "z" (which is a scalar) like:

Determinant of (Identity_matrix[5] - A1*z - A2*(z^2)) = 0

Here A1 and A2 are 2 separate given square matrices of length 5.

I have faced this problem while solving the characteristic polynomial
of a multivariate time series model. I am aware of the capability of
Mathematica for it's symbolic computation.

It would really be helpful if somebody helps me how to do that using
Mathematica.

Thanks and regards,