# minimal polynomial

## minimal polynomial

[′min·ə·məl ‚päl·ə′nō·mē·əl]
(mathematics)
The polynomial of least degree which both divides the characteristic polynomial of a matrix and has the same roots.
References in periodicals archive ?
A minimal polynomial of a value a is the polynomial m of lowest degree such that a is a root of m.
Clearly there exists a polynomial pd([lambda]) of degree d, called the minimal polynomial of v with respect to A, such that pd(A)v = 0.
In the current study, we consider using the minimal polynomial extrapolation (MPE) method which is one of the efficient polynomial-type methods.
In the remaining case, we use the machinery of analytic combinatorics to determine the minimal polynomial of its generating function, and deduce its growth rate.
For n [greater than or equal to] 3 let [[PSI].sub.n] be the minimal polynomial of 2cos(2[pi]/n} over Q.
Let [beta] be a Pisot series with minimal polynomial
This we hope will give us the minimal polynomial for m.
A digraph is nonderogatory if the characteristic polynomial and minimal polynomial of its adjacency matrix are equal.
(2) F' = F(y), whose minimal polynomial over F is [phi](T), where [phi](T) is defined as (1), for some u [member of] F.
Our approach is the following: from the minimal polynomial n of the CA T (or any other polynomial fulfilling [GAMMA](T) = 0) we derive a recursion relation for the [[T.sup.y].sub.x]s, the coefficients in [u.sup.x] of [T.sup.y].
The PN-based FSONN design activities have focused over the past years on the development of self-organizing, minimal polynomial networks with good generation capabilities.
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