In this paper, we first coneider the problelm as follow:Find a circulant matrix X∈CIRn×n such that for given matrics A,X∈Cn×m we have min || AX - B ||The existence theorems are obtained,and a general representation of such a matrix is presented. We denote the set of such ma- trices by SE. Then the matrix approximation problem is discussed. That is: Find a matrixX∈ SE such that for a given X∈ CIRn×n X∈CIRn×nwe have minX∈SE||X-X*||=||X-X*|| Where ||·|| is the Frobenius norm of matrics. We show that the approximation matrix is unique and provide...