NONNEGATIVE INTEGRAL MATRICES HAVING GENERALIZED INVERSES Kang, Kyung-Tae; Beasley, LeRoy B.; Encinas, Luis Hernandez; Song, Seok-Zun;
For an nonnegative integral matrix A, a generalized inverse of A is an nonnegative integral matrix G satisfying AGA = A. In this paper, we characterize nonnegative integral matrices having generalized inverses using the structure of nonnegative integral idempotent matrices. We also define a space decomposition of a nonnegative integral matrix, and prove that a nonnegative integral matrix has a generalized inverse if and only if it has a space decomposition. Using this decomposition, we characterize nonnegative integral matrices having reflexive generalized inverses. And we obtain conditions to have various types of generalized inverses.