- #1
Bacle
- 662
- 1
Hi, everyone:
I have been curious for a while about the similarity between the correlation
function and an inner-product: Both take a pair of objects and spit out
a number between -1 and 1, so it seems we could define a notion of orthogonality
in a space of random variables, so that correlation-0 random variables are orthogonal.
Does anyone know how far we can take this analogy, i.e., can we use correlation
as an inner-product to define a norm ( autocorrelation Corr(X,X)), and therefore
a normed space.?
Thanks.
I have been curious for a while about the similarity between the correlation
function and an inner-product: Both take a pair of objects and spit out
a number between -1 and 1, so it seems we could define a notion of orthogonality
in a space of random variables, so that correlation-0 random variables are orthogonal.
Does anyone know how far we can take this analogy, i.e., can we use correlation
as an inner-product to define a norm ( autocorrelation Corr(X,X)), and therefore
a normed space.?
Thanks.