A condition for the strong regularity of matrices in the minimax algebra

Columns of a matrix A in the minimax algebra are called strongly linearly independent if for some b the system of equations A?x = b is uniquely solvable (cf. 3]). This paper presents a condition which is necessary and sufficient for the strong linear independence of columns of a given matrix in the minimax algebra based on a dense linearly ordered commutative group. In the case of square matrices an O(n³) method for checking this property as well as for finding at least one b such that A?x = b is uniquely solvable is derived. A connection with the classical assignment problem is formulated.