An
operator ''A'' on an (infinite dimensional)
Banach space
In mathematics, more specifically in functional analysis, a Banach space (pronounced ) is a complete normed vector space. Thus, a Banach space is a vector space with a metric that allows the computation of vector length and distance between vector ...
or
Hilbert space
In mathematics, Hilbert spaces (named after David Hilbert) allow generalizing the methods of linear algebra and calculus from (finite-dimensional) Euclidean vector spaces to spaces that may be infinite-dimensional. Hilbert spaces arise natural ...
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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