The influence matrix method of enforcing incompressibility in pseudospectral simulations of fluid dynamics, as described by Kleiser and Schumann for channel flow, is generalized to other geometries, A formalism of projection and matrix operators is introduced, in which the influence matrix method is shown to be an application of the classic Sherman-Morrison-Woodbury formula of numerical linear algebra. Special attention is paid to the tau correction. Applications to Cartesian geometries illustrate the concepts and highlight the role of symmetry. A coded implementation in a cylindrical geometry, requiring special treatment of coordinate singularities, is used to investigate properties of the influence matrix and to provide estimates of timings.