Problem 6 By considering the commutator, show that the following Hermitian matrices may be |simultaneously diagonalized. Find the eigenvectors common to both and verify that under a unitary transformation to this basis, both matricies are diagonalized 2 1 0 1 1 1 (4) 0 0 0 1 -1 2 1 0 1 -1 Since is degenerate and A is not, you must be prudent in deciding which matrix dictates the choice of basis
Problem 6 By considering the commutator, show that the following Hermitian matrices may be |simultaneously diagonalized. Find the eigenvectors common to both and verify that under a unitary transformation to this basis, both matricies are diagonalized 2 1 0 1 1 1 (4) 0 0 0 1 -1 2 1 0 1 -1 Since is degenerate and A is not, you must be prudent in deciding which matrix dictates the choice of basis
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Transcribed Image Text:Problem 6 By considering the commutator, show that the following Hermitian matrices may be
|simultaneously diagonalized. Find the eigenvectors common to both and verify that under a unitary
transformation to this basis, both matricies are
diagonalized
2
1 0 1
1
1
(4)
0 0 0
1
-1
2
1 0 1
-1
Since is degenerate and A is not, you must be prudent in deciding which matrix dictates the choice
of basis
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