Unformatted text preview: primitive n th root of unity .) (iii) Why do we stop the index at k = n1? What is z n , z n +1 ? (iv) Plot these n solutions z , z 1 ,...,z n1 in the the complex plane for (i) n = 2; (ii) n = 3; (iii) n = 4; (iv) for a general n . (Use the one separate plane for each n ). b) Let w = e 2 πi/n be the primitive n th root of unity. Consider the matrix U = 1 √ n [ w jk ] j,k =0 , 1 ,...,n1 which is, in fact, the Fourier Matrix: U = 1 √ n 1 1 1 ··· 1 1 w w 2 ··· w n1 1 w 2 w 4 ··· w 2( n1) . . . . . . . . . . . . 1 w n1 w 2( n1) ··· w ( n1) 2 TRUE or FALSE: U is unitary. Justify your answer. 1...
View
Full Document
 Spring '12
 COSTIN
 Determinant, Matrices, Complex number, Orthogonal matrix, Unitary matrix, Identity matrix, identity matrix unitary

Click to edit the document details