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njuclean
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I'm learning "the transformation optics" and the first document about this method is "Photonic band structures" ( Pendry, J. B. 1993). In this document, the transfer matrix T is non-hermitian, Ri and Li are the right and left eigenvectors respectively.
Pendry defined a unitary matrix S=[tex]\sum[/tex]RiLi, here RiLi is the outer product between the right eigenvector and the left eigenvector. Then T can be diagonalized through STS-1.
I remember that the sum of the outer product between the right eigenvector and the left eigenvector is the unit matrix, so i cannot understand how can the unitary matrix S diagonalize T. Who can tell me what's wrong in my understanding?
Pendry defined a unitary matrix S=[tex]\sum[/tex]RiLi, here RiLi is the outer product between the right eigenvector and the left eigenvector. Then T can be diagonalized through STS-1.
I remember that the sum of the outer product between the right eigenvector and the left eigenvector is the unit matrix, so i cannot understand how can the unitary matrix S diagonalize T. Who can tell me what's wrong in my understanding?
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