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arXiv · 1110.4564

Z-matrix equations in max algebra, nonnegative linear algebra and other semirings

Peter Butkovic·Hans Schneider·Sergei Sergeev
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Abstract

We study the max-algebraic analogue of equations involving Z-matrices and M-matrices, with an outlook to a more general algebraic setting. We show that these equations can be solved using the Frobenius trace down method in a way similar to that in non-negative linear algebra, characterizing the solvability in terms of supports and access relations. We give a description of the solution set as combination of the least solution and the eigenspace of the matrix, and provide a general algebraic setting in which this result holds.

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Peter Butkovic, Hans Schneider, Sergei Sergeev. 2012-06-06. Z-matrix equations in max algebra, nonnegative linear algebra and other semirings. https://doi.org/10.1080/03081087.2012.65107

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