Generalization of the matrix inversion lemma

A generalized form of the matrix inversion lemma is shown which allows particular forms of this lemma to be derived simply. The relationships between this direct method for solving linear matrix equations, lower-diagonal-upper decomposition, and iterative methods such as point-Jacobi and Hotelling's method are established. The generalized form is used to derive a new factorization scheme and a new matrix inversion algorithm with a high degree of parallelism.