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Annihilating polynomial

From Wikipedia, the free encyclopedia

A polynomial P is annihilating or called an annihilating polynomial in linear algebra and operator theory if the polynomial considered as a function of the linear operator or a matrix A evaluates to zero, i.e., is such that P(A) = 0.

Note that all characteristic polynomials and minimal polynomials of A are annihilating polynomials. In fact, every annihilating polynomial is the multiple of the minimal polynomial of an operator A.[1][2]

See also

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References

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  1. ^ Taboga, Marco. "Minimal Polynomial". statlect.com. Retrieved 17 November 2023.
  2. ^ Hoffman, K., Kunze, R., "Linear Algebra", 2nd ed., 1971, Prentice-Hall. (Definition on page 191 of section 6.3)