Nonnegative integral matrices having generalized inverses
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For an m×n nonnegative integral matrix A, a generalized in- verse of A is an n×m nonnegative integral matrix G satisfying AGA = A. In this paper, we characterize nonnegative integral matrices having gen- eralized 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 decom- position, we characterize nonnegative integral matrices having reflexive generalized inverses. And we obtain conditions to have various types of generalized inverses.
Abstract
For an m×n nonnegative integral matrix A, a generalized in- verse of A is an n×m nonnegative integral matrix G satisfying AGA = A. In this paper, we characterize nonnegative integral matrices having gen- eralized 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 decom- position, we characterize nonnegative integral matrices having reflexive generalized inverses. And we obtain conditions to have various types of generalized inverses.
참고문헌 (6)
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