Hermitian matrices and unitary similarity transformations

[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

 

[tiny-tim]

Hi Shyan!

What's B doing there? ​

 

[ShayanJ]

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

 

[tiny-tim]

But A is the matrix which undergoes the similarity transformation.