The Improved Nonsingularity on the r-Circulant Matrices in Signal Processing

As an important class of special matrix, 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 [1] and [2], we discuss the inverse problem of circulant matrices, by using only the elements in the first row of the r-circulant matrix on non singularity, we give some discriminations, give a simpler and more useful algorithm method of the inverse matrix of the circulant matrix. and give an example at last.