I know that when two random vectors are independent, they are uncorrelated. The opposite it isn't true necessarily.

What about orthogonal random vectors??

Orthongonality implies independence??

Independence implies orthogonality?

Why??

i know for example, that orthogonality exists when the correlation matrix is diagonal, and uncorrelation exists when covariance matrix is diagonal. But i don't understand clearly the relation with independence...

It's a little confusing to me... Thanks....