Cyclic vector

In the mathematics of operator theory, an operator A on an (infinite dimensional) Banach space or Hilbert space H has a cyclic vector f if the vectors f, Af, A2f,... span H. Equivalently, f is a cyclic vector for A in case the set of all vectors of the form p(A)f, where p varies over all polynomials, is dense in H.[1][2]This abstract algebra-related article is a stub.You can help Wikipedia by expanding it.
operator theoryoperatorBanach spaceHilbert spaceCyclic and separating vectorabstract algebra