Cyclic vector

In the mathematics of operator theory, an operator A {\displaystyle A} on an (infinite-dimensional) Banach space or Hilbert space H {\displaystyle H} has a cyclic vector f {\displaystyle f} if the vectors f , A f , A 2 f , … {\displaystyle f,Af,A^{2}f,\dots } span H {\displaystyle H} . Equivalently, f {\displaystyle f} is a cyclic vector for A {\displaystyle A} in case the set of all vectors of the form p ( A ) f {\displaystyle p(A)f} , where p {\displaystyle p} varies over all polynomials, is dense in H {\displaystyle H} .^[1][2]

See also

• Cyclic and separating vector

References