Dimension group of a non-negative integer irreducible matrix Original Research Article

In this paper we are concerned with a non-negative integer and irreducible matrix image. The main contribution is to prove that if the matrix satisfies certain spectral and algebraic constraints, the cone:imageis defined by linear maps image, in the sense that v set membership, variant C is equivalent to, phil(v) greater-or-equal, slanted 0 for all l = 0, … , k − 1 (where k is the index of cyclicity of the irreducible matrix). This result allows us to characterize the dimension group generated by the matrix, it is a subgroup of image endowed with an order induced by the positive cone of image.