> The result is zero if the signals are orthogonal (like the dot product of two vectors in 2D or 3D that are at 90 degrees).
Here is a bit more rambling in the direction of linear algebra and probability: you can define a vector space on the set of all random variables, wherein each random variable is a vector. Once you do so, you can further impose an inner product space with the traditional covariance function as the inner product. If the two random variables are orthogonal with respect to this inner product and this space, by definition their covariance is equal to 0. It follows by the definition of correlation from covariance that their correlation will also be 0, i.e. orthogonality implies two variables are uncorrelated in this space :)
Strictly speaking the correlation function is not the inner product in this instance, but practically the result is the same.
Here is a bit more rambling in the direction of linear algebra and probability: you can define a vector space on the set of all random variables, wherein each random variable is a vector. Once you do so, you can further impose an inner product space with the traditional covariance function as the inner product. If the two random variables are orthogonal with respect to this inner product and this space, by definition their covariance is equal to 0. It follows by the definition of correlation from covariance that their correlation will also be 0, i.e. orthogonality implies two variables are uncorrelated in this space :)
Strictly speaking the correlation function is not the inner product in this instance, but practically the result is the same.