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'', ''A''<sup>2</sup>''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'''.<ref>{{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 }}</ref><ref>{{cite web |title=Cyclic vector |url=http://www.encyclopediaofmath.org/index.php?title=Cyclic_vector&oldid=34882 |website=Encyclopedia of Mathematics}}</ref>
==See also== * Cyclic and separating vector
==References== {{reflist}}
Category:Abstract algebra Category:Functional analysis
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