科研之友
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摘要
A classical finite dimensional result of Berman and Plemmons says that a nonnegative matrix with a nonnegative reflexive generalized inverse has a nonnegative rank factorization. In this article, we propose a notion of nonnegative rank factorization that is applicable in the infinite dimensional setting over more general cones and prove an infinite dimensional generalization of Berman and Plemmons's result. As a consequence, a simpler proof of the finite dimensional result (on the existence of nonnegative rank factorizations) is obtained. Characterizations of nonnegativity of the group inverse (when it exists) in infinite dimensions are also presented.
- 出版日期2010-9
