Question: Let A = 2 1 i 1 + i 1 Two by two matrix. (a) Find the eigenvalues of A (b) Find the eigenvectors of

Let A = 2 1 i

1 + i 1

Two by two matrix.

(a) Find the eigenvalues of A

(b) Find the eigenvectors of A: u1 and u2

(c) Normalize u1 and u2

(d) Form a matrix U = [u1, u2] based on your results from (c)

(e) Find U H U

(f) Find U HAU

(g) What can you say about the matrix U and relation to the matrix A

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