I have a matrix representation phi: G -> GL(d,C) and make a direct sum with its complex conjugate, how do I prove that this sum is matrix representation of G over RR?

Deja Bradshaw

Deja Bradshaw

Answered question

2022-10-29

I have a matrix representation ϕ: G G L ( d , C ) and make a direct sum with its complex conjugate, how do I prove that this sum is matrix representation of G over R ? I would perhaps prove equivalence with some real matrix representation ψ: ϕ: G G L ( 2 d , R ), but just don´t know the steps.

Answer & Explanation

Phoebe Medina

Phoebe Medina

Beginner2022-10-30Added 17 answers

Hint:
1 2 ( I i I i I I ) ( A + i B 0 0 A i B ) ( I i I i I I ) = ( A B B A ) .

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