1. The problem statement, all variables and given/known data Consider the vector space of continuous, complex-valued functions on the interval [−∏, ∏]. Show that defines a scalar product on this space. Are the following functions orthogonal with respect to this scalar product? 2. Relevant equations 3. The attempt at a solution Definition of scalar product: A scalar product is an operation that assigns a complex number to any given pair of vectors |a> and |b> belonging to a LVS. Case 1: f(t) and g(t) are equal => integrand is real => scalar product is real Case 2: f(t) and g(t) are not equal => integrand is complex => scalar product is complex I'm not sure if this shows that the function is a scalar product. Is there a more mathematically rigorous way of showing it?