Some Problems On Circulant Matrices

The circulant matrices is a special matrix which is very important, at present, it has become a very important research direction in matrix theory and fundamental mathematics, and has been widely concerned by scholars.We study some problems on algorithm to compute the square roots of r-circulant matrices and the power for symmetric circulant matrices of n order and the power for anti-tridiagonal matrices of even order. The detail is as follows:1. Based on the methods of finding the square roots of circulant matrices, it has been promoted to the r-circulant matrices, the algorithm computing the square roots of r-circulant matrices are given.2. Related issues on symmetric circulant matrices of n order is discussed, and the general expression for the entries of the qth power (q∈N) for one type of symmetric circulant matrices is derived.3. The power of the even order and anti-double0-circulant matrices Ais studied, according to the relevant results which is existed, and the general expression for the entries of the/th power (l∈N)for one type of anti-double0-circulant matrices Aof even order is given.