In this paper we study the Cartan matrix associated to the Ext-projective stratifying system induced by a basic and τ-rigid object M in mod (A) by means of the g-vectors of the indecomposable direct summands of M. In particular we show that the Cartan group of a stratifying system associated to a τ-rigid module can be calculated directly using these vectors. Moreover we characterise the stratifying systems coming from τ-rigid modules that have a diagonal Cartan matrix.