Nonnegative matrices \(A\) with \(AA^\#\geqslant 0\).
This paper deals with nonnegative matrices \(A\) having group inverse \(A^\#\) satisfying certain nonnegativity property. Concretely, the class of nonnegative matrices \(A\in\mathbb{R}^{n\times n}\) such that \(AA^\#\geq 0\) is characterized. The relationship with nonnegative matrices such that \(A^\#\geq 0\) is analyzed. Finally, nonnegative matrices \(A\in\mathbb{R}^{n\times n}\) such that \(A-A^2\geq 0\) are studied.
scientific article; zbMATH DE number 2056697