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REPRESENTATIONS FOR THE GENERALIZED INVERSE OF SUMS OF MATRICES,
WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
Representations for the generalized inverse of the matrix sum AB CD are developed, where A and C are arbitrary matrices with complex elements. B and D are the transposed conjugates of A and C respectively. These representations are obtained using forms for the generalized inverse of partitioned matrices M A, B. Corresponding representations are obtained for the matrix sum A B in which A and B satisfy the condition AD theta. Computational forms for constructing the generalized inverse of any matrix X by application of results obtained for AB CD are discussed.