Affine dependence (${\sum }_i{\lambda }_i{x}_i=0,{\sum }_i{\lambda }_i=0$)

An affine dependence of points is a nonzero coefficient family satisfying the displayed identities. Equivalently, the augmented vectors $(x_i,1)$ are linearly dependent. Both identities are independent of the chosen origin. The absence of an affine dependence is affine independence.