monic polynomial


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Related to monic polynomial: monic equation, Irreducible polynomial

monic polynomial

[¦mō·nik ‚päl·ə′nō·mē·əl]
(mathematics)
A polynomial in which the coefficient of the term of highest degree is +1 and the coefficients of the other terms are integers.
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This implies that we can as well look at the monic polynomial p(x)/a = [p.
n](x), which applies more generally to the coefficients of any monic polynomial f(x) in Z[x].
A sequence of monic polynomials [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.
n] (x) is the classical monic polynomial, orthogonal with respect to the classical weight w (x).
n[greater than or equal to]0] be a monic polynomial sequence (MPS), deg [B.
To justify this claim, the main things to note are that (a) a monic polynomial that is irreducible over Z is also irreducible over [Z.
Notice that a linear functional u is said to be regular [4, 7] if there exists a monic polynomial sequence (MPS) [{[B.
n](z), the nth monic polynomial orthogonal with respect to [L.
In other words, the monic polynomial of degree n which best approximates the zero function on the interval [-1,1] according to the Chebyshev (minimax) norm, is a scaled Chebyshev polynomial.
n] provided that the norm of its product with a monic polynomial is given.
n-k,R]) and u is a monic polynomial of degree k [member of] {1, .
The minimal polynomial of A for V is the nonzero monic polynomial of lowest degree such that P(A)V = 0.