Quasidirect addition of matrices and generalized inverses (Q1308438)

The authors examine an additive rank property for a sum of matrices, which they call a quasidirect addition or, if the sum is given, a quasidirect decomposition. Intimately connected with this decomposition are certain (1,2)-inverses of the sum. They characterize quasidirect decompositions, and give some applications. Next, the authors specialize the condition to matrices which are unitarily quasidirect, and also characterize these matrix sums and their connection with the Moore- Penrose inverse. Finally, the authors introduce a matrix projector which is associated with a given rectangular matrix \(A\) and a generalized inverse of \(A\).