08. In a three-dimensional vector space, consider the operator whose matrix, in an orthonormal basis {11 >, 12 >,13 >}, is A = (0 -1 0) \1 0 (a) Is A Hermitian? Calculate its eigenvalues and the corresponding normalized eigenvectors. Verify that the eigenvectors corresponding to the two nondegenerate eigenvalues are orthonormal. (b) Calculate the matrices representing the projection operators for the two nondegenerate eigenvectors found in part (a).
08. In a three-dimensional vector space, consider the operator whose matrix, in an orthonormal basis {11 >, 12 >,13 >}, is A = (0 -1 0) \1 0 (a) Is A Hermitian? Calculate its eigenvalues and the corresponding normalized eigenvectors. Verify that the eigenvectors corresponding to the two nondegenerate eigenvalues are orthonormal. (b) Calculate the matrices representing the projection operators for the two nondegenerate eigenvectors found in part (a).
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Transcribed Image Text:08. In a three-dimensional vector space, consider the operator whose matrix, in an orthonormal
basis {11 >, 12 >,13 >}, is A = (0 -1 0)
\1 0
(a) Is A Hermitian? Calculate its eigenvalues and the corresponding normalized
eigenvectors. Verify that the eigenvectors corresponding to the two nondegenerate
eigenvalues are orthonormal.
(b) Calculate the matrices representing the projection operators for the two nondegenerate
eigenvectors found in part (a).
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