Cyclic vector
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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^2f,\dots 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 .
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^2f,\dots 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 . ==See also== Cyclic and separating vector ==References==
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