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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

Pendry defined a unitary matrix

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

**is non-hermitian,***T**R*_{i}and*L*_{i}are the right and left eigenvectors respectively.Pendry defined a unitary matrix

*=[tex]\sum[/tex]***S****R**_{i}**L**_{i}, here**R**_{i}**L**_{i}is the outer product between the right eigenvector and the left eigenvector. Then**can be diagonalized through***T***S****T****S**^{-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

*diagonalize***S***. Who can tell me what's wrong in my understanding?***T**
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