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I want to prove that if two hermitian matrices say $H_1$ and $H_2$ have the same spectra, then one of them is conjugate of the other by some unitary matrix.

$$H_1 = U H_2 U^{\dagger}$$

Any idea?

Jean Marie
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hossein mohammadi
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  • Can you add some context? Where is this problem from? What's a Hermitian Matrix? – Mason Dec 04 '18 at 19:33
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    Of course $H_1, H_2$ must have the same spectrum counting multiplicity. You are talking about the so-called "spectral theorem" ... https://en.wikipedia.org/wiki/Spectral_theorem – GEdgar Dec 04 '18 at 19:38

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