On Nonsingularity the Symmetric r-Circulant Matrices

Since symmetric r-circulant matrices have wide application, such as in numerical computation, signal processing, coding theory and oil investigation people have pay more and more attention to them in recent years. In this paper, motivated by, we give some discriminations by using only the elements in the first row of the symmetric r-circulant matrix on non singularity, and show the feasibility of these methods by an example.