A condition for the strong regularity of matrices in the minimax algebra (Q1082274)

Columns of a matrix A in the minimax algebra are called strongly linearly independent if for some b the system of equations \(A\otimes x=b\) is uniquely solvable. This paper presents a condition which is necessary and sufficient for the strong linear independence of columns of a give matrix in the minimax algebra based on a dense linearly ordered commutative group. In the case of square matrices an \(O(n^ 3)\) method for checking this property as well as for finding at least one b such that \(A\otimes x=b\) is uniquely solvable is derived. A connection with the classical assignment problem is formulated.