In quantum theory, it is also possible for an operator to have a non-discrete spectrum, such as the position operator formula_25 in quantum mechanics. This operator has a completely continuous spectrum, with eigenvalues and eigenvectors depending on a continuous parameter, formula_26. Specifically, the operator formula_25 acts on a spatial vector formula_28 as formula_29. In this case, the vector formula_11 can be written as a complex-valued function formula_31 on the spectrum of formula_25 (usually the real line). This is formally achieved by projecting the state vector formula_33 onto the eigenvalues of the operator, as in the discrete case formula_34. It happens that the eigenvectors of the position operator form a complete basis for the vector space of states, and therefore obey a closure relation: