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.

 

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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@jhmi.edu> rvaradhan@jhmi.edu

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