[R] Computing the minimal polynomial or, at least, its degree
Spencer Graves
spencer.graves at pdf.com
Fri Dec 3 17:13:27 CET 2004
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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--
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