A generalized inverse ∈-algorithm for constructing intersection projection matrices, with applications

Givenk linear manifolds ℳ1, ..., ℳk and corresponding perpendicular projection matricesP1, ...,Pk, a closed formula is derived for the perpendicular projection matrix with range. The derivation uses results taken from the theory of generalized inverses together with an application ofWynn'sε-Algorithm to a convergent sequence of matrices. A variant of this formula is then used in solving arbitrary complex linear systems by iteration and in computing generalized inverses; the latter application provides a solution to least squares linear regression problems.