On Cone-Monotonicity of Complex Matrices
Adi Ben-Israel · SIAM Review · 1970
Such matrices and operators are of great importance in numerical analysis [2, Chap. 3]. For m = n, (1) is equivalent to the existence and nonnegativity of A-1 [2, p. 376]. Rectangular real matrices of monotone kind were studied in [3] where, inter alia, (1) was proved equivalent to the existence of a nonnegative left inverse of A. These results are extended below to complex matrices. A pair {A, B} of complex matrices is monotone with respect to the pair {S, T} of closed convex cones (in the corresponding complex spaces) if