Minimal polynomial

English

Noun

1. Template:Lb 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.

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   • 1965 [John Wiley], Robert B. Ash, Information Theory, 1990, Dover, page 161,

     A procedure for obtaining the minimal polynomial of the matrix $T^i$, without actually computing the powers of $T$ is indicated in the solution to Problem 5.9.

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   • 2007, A. R. Vasishta, Vipin Vasishta, A.K. Vasishta, Abstract and Linear Algebra, Krishna Prakashan Media, 3rd Edition, page CA-439,

     Theorem 1. The minimal polynomial of a matrix or of a linear operator is unique.

2. Template:Lb 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.
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Translations

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See also

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Further reading

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• Matrix Minimal Polynomial on Template:W
• Algebraic Number Minimal Polynomial on Template:W
• minimal polynomial Template:W