Hermitian matrices and unitary similarity transformations

1. Feb 1, 2012

ShayanJ

I tried to prove that a hermitian matrix remains hermitian under a unitary similarity transformation.I just could do it to he point shown below.Any ideas?

$[ ( U A U ^ {\dagger}) B ] ^ {\dagger} = B ^ {\dagger} (U A U ^ {\dagger}) ^ {\dagger} = B (U A^ {\dagger} U ^ {\dagger})$

thanks

2. Feb 1, 2012

tiny-tim

Hi Shyan!

What's B doing there?

3. Feb 1, 2012

ShayanJ

Isn't B the hermitian matrix which should remain hermitian?

4. Feb 1, 2012

tiny-tim

But A is the matrix which undergoes the similarity transformation.

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