Cyclic vector explained

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]}

See also

• Cyclic and separating vector

Notes and References

1. Book: A Hilbert Space Problem Book . 19 . 86–89 . 10.1007/978-1-4684-9330-6_18 . Cyclic Vectors . Graduate Texts in Mathematics . 1982 . Halmos . Paul R. . 978-1-4684-9332-0 .
2. Web site: Cyclic vector . Encyclopedia of Mathematics.