Proving the Sum of Hermitian Matrices is Hermitian

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SUMMARY

The sum of two Hermitian matrices A and B is indeed Hermitian. This is proven by showing that the transpose of the sum equals the conjugate of the sum, specifically A + B = (A + B)*. The proof involves using the properties of conjugation and transposition, confirming that the operation holds true for Hermitian matrices. The discussion clarifies a minor typographical error regarding the notation used in the proof.

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chuy52506
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Prove that the sum of two hermitian matrices A and B gives us a hermitian matrix.

I'm not sure if this is a legit proof:
A+B=A*+B*
=(conjugate of A)T+(conjugate of B)T
=(conjugate(A+B))T
=(A+B)T
 
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It's fine. You need to replace that last T with a *, but I assume that was just a typo.
 

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