Английская Википедия:Annihilating polynomial

Материал из Онлайн справочника
Перейти к навигацииПерейти к поиску

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

References

Шаблон:Reflist

  1. Шаблон:Cite web
  2. Hoffman, K., Kunze, R., "Linear Algebra", 2nd ed., 1971, Prentice-Hall.(Definition on page 191 of section 6.3)