What is done first is, we are able to compute the matrix elements of the would-be operator formula_356, that is, we compute the quadratic form formula_357. It turns out that as formula_357 is a graph changing, diffeomorphism invariant quadratic form it cannot exist on the kinematic Hilbert space formula_359, and must be defined on formula_360. Since the master constraint operator formula_356 is densely defined on formula_362, then formula_356 is a positive and symmetric operator in formula_362. Therefore, the quadratic form formula_357 associated with formula_356 is closable. The closure of formula_357 is the quadratic form of a unique self-adjoint operator formula_368, called the Friedrichs extension of formula_356. We relabel formula_368 as formula_356 for simplicity.