  This paper presents some of the basic properties of conditioned observables
in finite-dimensional quantum mechanics. We begin by defining the sequential
product of quantum effects and use this to define the sequential product of two
observables. The sequential product is then employed to construct the
conditioned observable relative to another observable. We then show that
conditioning preserves mixtures and post-process of observables. We consider
conditioning among three observables and a complement of an observable.
Corresponding to an observable, we define an observable operator in a natural
way and show that this mapping also preserves mixtures and post-processing.
Finally, we present a method of defining conditioning in terms of self-adjoint
operators instead of observables. Although this technique is related to our
previous method it is not equivalent.
