A vector $x \in \mathcal{H}$ is a cyclic vector if $\mathcal{M}x$ is dense in $\mathcal{H}$.

Properties

The notions of cyclic vector is dual to that of separating vector with respect to the commutant$\mathcal{M}'$, that is a vector is cyclic for $\mathcal{M}$ iff it is separating for $\mathcal{M}'$.