I'm trying to prove that if A is a positive definite Hermitian matrix, <x,y>' = <Ax,y> defines an inner product.
So far I've only got
I'm having trouble with proving the rest. Any help will be greatly appreciated!
Well, the usual definition of positive definite Hermitian matrix is precisely that , with the complex conjugate transpose of the vector , and from here you get positiviness. , and you get skew-linearity...