Thus, unless B ^ ^ and O ^ ^ share and identical set of eigenstates (that is to say, { | φ φ i ⟩ ⟩ } = { | ω ω i ⟩ ⟩ } ), the initial measurement fundamentally influences the system to affect future measurements. This statement is identical to stating that if the commutator of the two observables is non-zero, repeated observations of the observables will present altered results. Observables will share the set of eigenstates if