A polynomial P is annihilating or called an annihilating polynomial in linear algebra and operator theory when the polynomial is applied to a linear operator or a matrix A such that P(A) = 0.

Note that all characteristic polynomials and minimal polynomials of A are annihilating polynomials. In fact, all multiples of the minimal polynomial A are annihilating polynomials.[1][2]

See also

References

  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)
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