Abstract
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( n 3) 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.
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