# Cyclic vector

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This article provides insufficient context for those unfamiliar with the subject. (October 2018) |

An operator *A* on an (infinite dimensional) Banach space or Hilbert space **H** has a cyclic vector *f* if the vectors *f*, *Af*, *A ^{2}f*,... 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[edit]

## References[edit]

**^**Halmos, Paul R. (1982). "Cyclic Vectors".*A Hilbert Space Problem Book*. Graduate Texts in Mathematics.**19**. pp. 86–89. doi:10.1007/978-1-4684-9330-6_18. ISBN 978-1-4684-9332-0.**^**"Cyclic vector".*Encyclopedia of Mathematics*.