The Directed Graph On Non-Negative Circulant Matrices

Circulant matrices are very special matrices with good properties and structures, which are an important component of the matrix theory and have become one of the most active and vital research fields in applied mathematics and can be widely used in other fields such as control theory[8-15],coding theory[16-18], molecule vibrations theory[19-22] and so on. In this paper, we mostly discuss the combination property of non-negative circulant matrices. Kim K. H and Krabill J. R have given the necessary and sufficient condition of determining the irreducibility on non-negative circulant matrices in [4]. Through constructing the corresponding circle group of the vertex, we mainly do some researches in the structure of the directed graph on non-negative circulant matrices by group theory and graph theory. Moreover, we also gain Kim K. H's result using a new method and give the expression of the permutation similar standard form on reducible non-negative circulant matrices.