Algorithms For Abitrary Roots Of Circulant Matrices

Circulant matrices, which are an important component of the matrix theory, have become one of the most important and active research fields of applied mathematics increasingly. In this paper, we introduce our some work in algorithms for mth arbitrary roots of circulant matrices . To start with, we prove the existence of the mth roots of circulant matrices . Next, we present circulant matrices including the classical circulant matrix, r - circulant matrix and scaled circulant factor matrices by linear equations. In addition, we obtain their number of the mth roots of circulant matrices. Finally , we analyse the computational complexity of this algorithm.