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unscientific
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Homework Statement
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?
Homework Equations
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?