minimal polynomial

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English[edit]

Noun[edit]

minimal polynomial (plural minimal polynomials)

  1. (linear algebra) Given a square matrix M over a field K, the minimal polynomial is the monic polynomial over K of smallest degree, which when applied to M yields the zero matrix.
  2. (field theory) Given a number α which belongs to some extension field of a field K and is algebraic over K, the minimal polynomial for α over K is the monic polynomial over K of smallest degree for which α is a root.