[R] Computing the minimal polynomial or, at least, its degree

[Spencer Graves]

      Have you looked at library(polynom)?  Will that with 
unique(eigen(A)$values) allow you to compute what you want? 

      hope this helps. 
      spencer graves

Ravi Varadhan wrote:

>Hi,
>
> 
>
>I would like to know whether there exist algorithms to compute the
>coefficients or, at least, the degree of the minimal polynomial of a square
>matrix A (over the field of complex numbers)? I don't know whether this
>would require symbolic computation.  If not, has any of the algorithms been
>implemented in R?  
>
> 
>
>Thanks very much,
>
>Ravi.
>
> 
>
>P.S.  Just for the sake of completeness, a minimal polynomial is a monic
>polynomial (whose leading coefficient is unity) of least degree, which
>divides all the annihilating polynomial of A. In particular, the minimal
>polynomial divides the characteristic polynomial.  Knowing the degree of the
>minimal polynomial is useful in characterizing the convergence properties of
>a certain class of numerical schemes for iteratively solving linear (and
>nonlinear) system of equations.
>
> 
>
>--------------------------------------------------------------------------
>
>Ravi Varadhan, Ph.D.
>
>Assistant Professor,  The Center on Aging and Health
>
>Division of Geriatric Medicine and Gerontology
>
>Johns Hopkins Univerisity
>
>Ph: (410) 502-2619
>
>Fax: (410) 614-9625
>
>Email:   <mailto:rvaradhan at jhmi.edu> rvaradhan at jhmi.edu
>
>--------------------------------------------------------------------------
>
> 
>
>
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-- 
Spencer Graves, PhD, Senior Development Engineer
O:  (408)938-4420;  mobile:  (408)655-4567