Annihilating polynomial
From HandWiki
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)
References
- ↑ Taboga, Marco. "Minimal Polynomial". https://www.statlect.com/matrix-algebra/minimal-polynomial.
- ↑ Hoffman, K., Kunze, R., "Linear Algebra", 2nd ed., 1971, Prentice-Hall.(Definition on page 191 of section 6.3)
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