2.2 KB · ⇊ 2 parts · ⤓ Micron 2.2 KB · ⤓ HTML 9.3 KB

top

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-ref-1[1]cite-ref-2[2]

• See also

• References

• Cyclic and separating vector

cite-note-11. ↑ citerefhalmos1982Halmos, Paul R. (1982). "Cyclic Vectors". A Hilbert Space Problem Book. Graduate Texts in Mathematics. Vol. 19. pp. 86–89. doi:10.1007/978-1-4684-9330-6_18. ISBN 978-1-4684-9332-0.

cite-note-22. ↑ "Cyclic vector". Encyclopedia of Mathematics.