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'',... 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
Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematically ...
in H.
See also
*
Cyclic and separating vector
References
Abstract algebra
Functional analysis
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