6. (20 points) An n x n circulant matrix C is given by CO C1 C2...

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6. (20 points) An n x n circulant matrix C is given by CO C1 C2 Cn-1 Cn-1 CO C1 Cn-2 C = Cn-2 Cn-1 Co Cn-3 C1 C2 C3 CO (16) For example, the permutation matrix (A permutation matrix is a square binary matrix that has exactly one entry of 1 in each row and each column and Os elsewhere.) 0 1 0 0 0 1 0 P = : 000 100 ... is a circulant matrix. Let (17) 1 f(x) = co+cA+. +Cn-1"-1, (18) show that C = f(P). (19) 6. (20 points) An n x n circulant matrix C is given by CO C1 C2 Cn-1 Cn-1 CO C1 Cn-2 C = Cn-2 Cn-1 Co Cn-3 C1 C2 C3 CO (16) For example, the permutation matrix (A permutation matrix is a square binary matrix that has exactly one entry of 1 in each row and each column and Os elsewhere.) 0 1 0 0 0 1 0 P = : 000 100 ... is a circulant matrix. Let (17) 1 f(x) = co+cA+. +Cn-1"-1, (18) show that C = f(P). (19)