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Solutions of Z-matrix equations. (English) Zbl 0652.15016
The solvability of the matrix equation \(Ax=b\), where A is a Z-matrix and b is a nonnegative vector is discussed. A previous existence theorem for a solution is reproved. The results are applied to study nonnegative vectors in the range of Z-matrices. It is a characteristic of the problem described above that the existence and the nature of a solution depend entirely on graph theoretic conditions. In the case that nonnegativity of the solution is not required, it is shown that there are no purely graph theoretic conditions for solvability but, however, there are graph theoretic results concerning the nature of the solution.
Reviewer: M.de la Sen

MSC:
15B48 Positive matrices and their generalizations; cones of matrices
15A06 Linear equations (linear algebraic aspects)
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