Let f = (123 ... n) be the full cycle permutation of the finite set X...

 

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Let f = (123 ... n) be the full cycle permutation of the finite set X = {1,..., n}. 1. Determine the eigenvalues and eigenvectors of the associated linear transformation er, as described in A8Q1, with the field being C. 2. Now let the field be Z/7Z, answer the same question and explain how the answer depends on n. Hint: look at this diagram: 2 • 1 4 3. Let f = (123 ... n) be the full cycle permutation of the finite set X = {1,..., n}. 1. Determine the eigenvalues and eigenvectors of the associated linear transformation er, as described in A8Q1, with the field being C. 2. Now let the field be Z/7Z, answer the same question and explain how the answer depends on n. Hint: look at this diagram: 2 • 1 4 3.