Question: Q3. Consider the matrix, A = 0 1 0 -1 0 0 (a) Find the eigenvalues 's (doubly degenerate) and the eigenvectors ({|a;)}, i

Q3. Consider the matrix, A = 0 1 0 -1 0 0

Q3. Consider the matrix, A = 0 1 0 -1 0 0 (a) Find the eigenvalues 's (doubly degenerate) and the eigenvectors ({|a;)}, i = 1,2,3) o the operator A. (b) Show that each of the sets |a), |a2), |a3) forms an orthonormal and complete basis. (c) Consider the matrix U which is formed from the normalized eigenvectors of A. Verify that U is unitary (UU = I). (d) Show that U satisfies the relation 121 0 0 U+AU = 0 22 0, 11, 12, 13 are the eigenvalues of A. 0 0 231

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