in this talk we make a (perhaps) unexpected link between the combinatorialnotion of partially ordered sets (posets) and certain families ofmatrices. using this link, we give a simple, matrix-based proof of themoebius inversion formula on a poset and a variant of it. it is thisvariant which is really at the heart of the talk, for it will allow us tosimultaneously analyze certain properties (determinant, inertia, etc.) ofentire families of matrices via their $ldl^t$-factorizations.refreshments will be provided