The Nonsingularity on the Symmetric r-Circulant Matrices

Circulant matrix is important since it is an active research field of applied mathematic and computation mathematic increasingly. R-circulant matrices have applied in numerical computation, signal processing, coding theory and oil investigation in recent years, and so on. In this paper, motivated by Zhaolin Jiang (1995), we give some discriminations by using only the elements in the first row of the r-circulant matrix in the diagonal matrix on non singularity, and give two examples at last.