Abstract
The tropical kernel of a Min-Plus matrix is a linear space. It has a finite basis that is uniquely determined up to scalar multiplication. In this paper, we give a characterization of vectors in a basis of the kernel using the tropical analogue of Cramer's rule. We first show that each finite vector in a basis can be obtained by applying Cramer's rule to a submatrix consisting of certain rows of the original matrix. We prove the main results by presenting an algorithm for choosing such rows. Further, we extend the result for kernel vectors that contain infinity in its entries.
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