Monotonicity and iterative approximations involving rectangular matrices
Robert J. Plemmons · Mathematics of Computation · 1972
A new characterization of row-monotone matrices is given and is related to the Moore-Penrose generalized inverse. The M M -matrix concept is extended to rectangular matrices with full column rank. A structure theorem is provided for all matrices A A with full column rank for which the generalized inverse A + ≧ 0 {A^ + } \geqq 0 . These results are then used to investigate convergent splittings of rectangular matrices in relation to iterative techniques for computing best least squares solutions to rectangular systems of linear equations.