Monotonicity and iterative approximations involving rectangular matrices

Plemmons, Robert J.

doi:10.1090/S0025-5718-1972-0315882-2

Monotonicity and iterative approximations involving rectangular matrices
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by Robert J. Plemmons PDF

Math. Comp. 26 (1972), 853-858 Request permission

Abstract:

A new characterization of row-monotone matrices is given and is related to the Moore-Penrose generalized inverse. The $M$-matrix concept is extended to rectangular matrices with full column rank. A structure theorem is provided for all matrices $A$ with full column rank for which the generalized inverse ${A^ + } \geqq 0$. 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.

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