# 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 ?
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.
Let [theta] be an algebraic integer, and f (x) the minimal polynomial of 9 over Q.
Let [beta] be a Pisot series with minimal polynomial
This we hope will give us the minimal polynomial for m.
The most popular vector extrapolation methods are the minimal polynomial extrapolation (MPE) method by Cabay and Jackson , the reduced rank extrapolation (RRE) method by Eddy  and Mesina , the modified minimal polynomial extrapolation (MMPE) method by Sidi et al.
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.
n](x), which is defined as the minimal polynomial over Q for any primitive nth root of unity [zeta] in C.
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.
Now we fix n = 85, all the 4-cyclotomic cosets mod 85 and minimal polynomial of [[alpha].
A ROOT object contains the minimal polynomial of the algebraic number and the root number, an integer indicating which of the roots of the minimal polynomial, the ROOT object represents.
Thus Kummer's theorem asserts h(x) = (x - b)(x + b + 1) mod p for the minimal polynomial h(x) of [theta].
Since [parallel]rn-1[parallel] = 0 implies that the degree of the minimal polynomial of A is[parallel][r.
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