On the solvability of homogeneous two-sided systems in max-algebra

A. Aminu
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 16, 2010, Number 2, Pages 5–15
Full paper (PDF, 247 Kb)


Authors and affiliations

A. Aminu
Department of Mathematical Sciences
Kano University of Science and Technology, Wudil
P.M.B 3244, Kano, Nigeria


Let ab = max(a, b) and ab = a+b for a, b ∈ ℝ and extend the pair of operations to matrices and vectors in the same way as in linear algebra. The homogeneous twosided system in max-algebra is of the form Ax = Bx. No polynomial method for solving homogeneous system is known. In this paper, we consider homogeneous twosided linear systems in max-algebra in a special case. We show that it can be checked in O(n3) time whether a given two-sided homogeneous system belongs to this special case. Solvability can be decided in O(n3) time and in the positive case a solution can be found in O(n3).


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Aminu, A. (2010). On the solvability of homogeneous two-sided systems in max-algebra, 16(2), 5-15.

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