The focus of this note is to highlight two relatively simple approaches to determine the matrix projection first introduced by Crowe et al. (1983) to solve data reconciliation problems when unmeasured variables exist. The first method uses recursive matrix inversion by partition where the second uses a modified Cholesky factorization. The purpose of the two algorithms is to identify dependent columns and rows in the topology matrix of the unmeasured variables where the matrix projection is then formulated. Although other methods are available to determine the nullity of a matrix such as QR factorization and singular value decomposition, it is preferred to use this identification procedure along with Crowe＇s matrix projection formulation because of its numerical efficiency, simplicity and interpretation. Two mass reconciliation examples are presented, one small and one large, to clarify and verify the techniques. (C) 1998 Elsevier Science Ltd. All rights reserved.