For the permutation of Example 6, write out the circulant matrix C = c0I + c1P + c2P 2 +
Chapter 5, Problem 5.5.24(choose chapter or problem)
For the permutation of Example 6, write out the circulant matrix C = c0I + c1P + c2P 2 + c3P 3 . (Its eigenvector matrix is again the Fourier matrix.) Write out also the four components of the matrix-vector product Cx, which is the convolution of c = (c0,c1,c2,c3) and x = (x0,x1,x2,x3).
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