On the regularity of matrices in min algebra

Abstract

We consider the concept of regularity for square matrices with entries from a linearly ordered commutative group ( G,+,⩾), the algebraic compositions being given by x ⊕ y= min( x, y), x⊗ y= x+ y. For the case where G is cyclic we derive a necessary and sufficient condition for the regularity of a matrix, which can be checked in O( n 3) operations using standard algorithms.