A matrix C is a table of coefficients; C zeta is the list of its row measurements. Its kernel consists of difference vectors xi satisfying C xi=0. Two vectors have the same measurements exactly when their difference is in this kernel. A linear output B zeta is therefore determined by C zeta whenever B xi=0 for every xi in the kernel. For example, C zeta=zeta_1+zeta_2 determines 3zeta_1+3zeta_2, but not zeta_1. In the construction, choose a linear map M that fixes the kernel: M xi=xi there. Then B=I-M vanishes on the kernel, so the correction (I-M)zeta is determined by the measurements. I denotes the identity map.