ABSTRACT
The inner product of any function with itself is >0 unless that function is identically equal to zero:
The parallel between the inner product defined here and the dot (or inner) product of two vectors is obvious. If (f, g)=0, the two functions are orthogonal.12 If there is a
set of functions , it is orthonormal if, for any i and j,
If a vector space has dimension n, there are (at most) n vectors that are mutually orthogonal.13 However, there can be an infinite number of different functions fj(x) that are mutually orthogonal. In this sense, a Hilbert space has a dimension that is infinite.
