This paper proposes to investigate the use of a coordinate free approach for the mapping of geometrical requirements along the product life cycle. The geometry of the studied assembly is represented using a Gram matrix that is derived from a parametric model constituted of points and vectors. This parametric model is updated for all the relevant phases of the product life cycle. More precisely, this paper demonstrates how to combine two Gram matrices used as coordinate free representations for two states of an assembly into a global one in order to map the geometrical requirement evolution. This association is carried out using the Cholesky factorization technique. The application presented in this paper is constituted of a simple 2D case.