Cyclic vector

"See also: Cyclic and separating vector"
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.