Simply--Prove that any Hermitian operator is linear
Hermitian operator defined by: int(f(x)*A*g(x)dx)=int(g(x)*A*f(x)dx)
Linear operator defined by: A[f(x)+g(x)]=Af(x)+Ag(x)
Where A is an operator
The Attempt at a Solution
I am at a complete loss of how to even start this. I know I need to get from int(f(x)*A*g(x)dx)=int(g(x)*A*f(x)dx) to A[f(x)+g(x)]=Af(x)+Ag(x) where A is the Hermitian operator, but I dont know how/what to manipulate to get here....