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A symmetric 4x4 matrix has 10 independent components.

Let's say that matrix describes graviton h_mu_nu.

In general I can bring any symmetric matrix to diagonal form, so if can and I bring my h_mu_nu matrix to diagonal form where it has only 4 independent components ... than what happens to the rest 6 components...does this diagonalizing procedure (which in some sense means rotation in space-time and fixing my frame of reference ) "consumes" degrees of freedom ?

Could you please advise...

Thank you

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# Degrees of freedom - matrix diagonalization

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