minimal polynomial

Definitions

1. 1

   For a given square matrix M over some field K, the smallest-degree monic polynomial over…

   For a given square matrix M over some field K, the smallest-degree monic polynomial over K which, when applied to M, yields the zero matrix.

   • 1965 [John Wiley], Robert B. Ash, Information Theory, 1990, Dover, page 161, A procedure for obtaining the minimal polynomial of the matrix Tⁱ, without actually computing the powers of T is indicated in the solution to Problem 5.9.
2. 2

   Given an algebraic element α of a given extension field of some field K, the monic…

   Given an algebraic element α of a given extension field of some field K, the monic polynomial of smallest degree of which α is a root.

   • […]we are given an element #92;alpha#92;inE, and want to compute the minimal polynomial #92;phi#92;inF#91;X#93; of #92;alpha over F.
   • Let #92;alpha be an algebraic number with degree n and let P be the minimal polynomial for #92;alpha (see Section 6.5).

The neighborhood