The study of some properties of a circulant matrix

Circulant matrix is a matrix of size nxn where the ith row elements for i = 1,2,3, …, n are obtained by shifting the first row elements to the right as much as i − 1 steps. The general form of the circular matrix can be expressed as follows Cnxn=[ c0c1c2…cn−1cn−1c0c1⋯cn−1c0⋮⋮⋱⋱⋱c1c1⋯cn−1⋯c0 ] This paper aims to study some of the properties of the transfosed circulant matrix from which the circulant matrix is circulant, the product of the circulant matrix is the circulant matrix and the circulant matrix is the normal matrix. Furthermore, the circular matrix can be diagonalized