Proving Inner Product with Hermitian Adjoint: A_hat

[mkt]

Hello, I'm a little bit confused regarding Hermitian Adjoint. I want to show that <x,y> = A(x,y) is an inner product where the function A : V*V --> V be defined as A(x,y) = x^T*A_hat*y. A_hat = [2 1 0; 1 4 1; 0 1 4].

How would i go about showing that <x,y> = A(x,y) is an inner product?

Note that <,> represents inner product

 

[Dick]

What are some properties of A(x,y) being an inner product that you would have to show? You really have to show some work first.