Annihilating polynomial explained

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

• Cayley–Hamilton theorem
• Minimal polynomial (linear algebra)

Notes and References

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