Abstract:Based on the general formula of generalized inverse matrix and Kelly inverse four block matrix, we analyze the existence conditions of a special kind of Kelly inverse four block matrix with a rank defective sub-block matrix in the upper left corner and a zero sub-block matrix in the lower right corner. The explicit expression formula of a Kelly inverse matrix of this kind is derived using the generalized inverting matrix method and the matrix transformation method, and is applied to the parameter estimation of rank-defective indirect adjustment model with constraints. The results show that when existence conditions are satisfied, the solution of rank-defective indirect adjustment model with constraints by inverting block matrix is consistent with that of the indirect adjustment model. This proves that the derived explicit expression formula is feasible.