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Hermitian Matrix

I need to prove that B = i(I+U)(I-U)^-1 where 'i' is the imaginary constant and I is the identity matrix - is a Hermitian matrix? How do I proceed? I've tried daggering it but I get U^-1 terms which I'm not sure how to deal with.

Gracias.
(edited 9 years ago)
Original post by Benjy100
I need to prove that B = i(I+U)(I-U)^-1 where 'i' is the imaginary constant and I is the identity matrix - is a Hermitian matrix? How do I proceed? I've tried daggering it but I get U^-1 terms which I'm not sure how to deal with.

Gracias.


Are you given any particular properties about U?
Reply 2
Original post by Slowbro93
Are you given any particular properties about U?


Sorry, I completely forgot to include that vital information, U is a unitary matrix, so U dagger = U inverse
Original post by Benjy100
I need to prove that B = i(I+U)(I-U)^-1 where 'i' is the imaginary constant and I is the identity matrix - is a Hermitian matrix? How do I proceed? I've tried daggering it but I get U^-1 terms which I'm not sure how to deal with.

Gracias.


Remember to use the properties of each identity:

For unitary matrices, U=UU=U^*

And in addition: (A)=A(A^*)^* = A

How can you use these two properties to help with your proof?

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