wa3 - eigenvalue? Exercise 2. What are the eigenvalues of Z...

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Winter 2011 Math 67 Linear Algebra Writting Assignment 3 Exercise 1. Consider the 4-by-4 matrix with complex entries X = x 1 x 2 x 3 x 4 x 4 x 1 x 2 x 3 x 3 x 4 x 1 x 2 x 2 x 3 x 4 x 1 . This is called a circulant matrix . Let ζ be a 4th root of unity (i.e., ζ 4 = 1). Prove that (1 ,ζ,ζ 2 3 ) is an eigenvector of X . What is the corresponding
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Unformatted text preview: eigenvalue? Exercise 2. What are the eigenvalues of Z = 1 1 0 0 0 1 1 0 0 0 1 1 1 0 0 1 ? Use your answer to prove that the eigenvectors in Exercise 1 are linearly in-dependent. 1...
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