It is possible to associate with each periodic sequence of

Question

Question: It is possible to associate with each periodic sequence of period N an N x N circulant matrix. This matrix is defined by taking the given values of the sequence as the first row of the matrix, and filling in the remaining rows by means of a cyclic shift of the first row. The matrix associated with 1 is

Prove that M_f.M_g = M_[f*g] and c₁M_f + c₂M_g = M_{[c1f + c2g]}, showing that the mapping from periodic sequences to circulant matrices is a ring homomorphism.