Dear Colleagues,
The polarisability matrix in orthogonal x-y coordinate system is symmetric.
But, as I transform the matrix to an oblique co-ordinate system, the matrix is no longer symmetric. I can't explain it physically.
Can anyone please help me to understand the physics of this. Why the matrix is no more symmetric in oblique co-ordinate system.
Thanks and Regards
N Das
Dear Nityananda Das,
i suggest you to see attached files on topic.
Best regards
You can think along these lines:
Under similiarity transformation of a square matrix A ( n by n), the characterstic polynomial is preserved, and thus the eigenvalues and their algebraic multiplicities. But even if A is square and hermitian, it would not retain hermiticity under all possible similarity transformations, under the class of Unitary similarity transformation both the characteristic polynomial and hermitian property is preserved.
Dear Nityananda Das
This discussion might be useful, have a look
https://physics.stackexchange.com/questions/473987/is-polarization-matrix-always-diagonalizable
Kind Regards
Qamar Ul Islam