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.
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.
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=U∗
And in addition: (A∗)∗=A
How can you use these two properties to help with your proof?