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.{{cite book |title=A Hilbert Space Problem Book |volume= 19 |pages= 86–89 |doi= 10.1007/978-1-4684-9330-6_18 |chapter= Cyclic Vectors |series= Graduate Texts in Mathematics |year= 1982 |last1= Halmos |first1= Paul R. |isbn= 978-1-4684-9332-0 }}{{cite web |title=Cyclic vector |url=http://www.encyclopediaofmath.org/index.php?title=Cyclic_vector&oldid=34882 |website=Encyclopedia of Mathematics}}