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Re: Determining the root of the characteristic equation for time


On 10/29/2010 3:26 AM, Christofer Bogaso wrote:
> 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,
>

may be something like this:

In[59]:= Clear[z];

n=5;
A1=Table[RandomReal[1],{i,5},{j,5}];
A2=Table[RandomReal[1],{i,5},{j,5}];

Solve[Det[IdentityMatrix[n]-A1*z-A2*(z^2)]==0,z]

Out[63]= 
{{z->-2.4021738242972597},{z->-1.340898151721915},{z->-0.8241488489166163-0.2913103890152045 
I},{z->-0.8241488489166163+0.2913103890152045 
I},{z->0.2868840290088525-1.8095777731669567 
I},{z->0.2868840290088525+1.8095777731669567 
I},{z->0.30173526317565597},{z->1.0027788027642381-0.527105585145346 
I},{z->1.0027788027642381+0.527105585145346 I},{z->2.005527612079525}}

--Nasser


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