Expected value of coupled signals is zero Suppose there are two vector signals, $u$ and $v$, which are functions of time. Given, $E[uv^T]=0$, what is the physical significance of this statement. For clarity, assume $u$ and $v$ are noises in a system like in kalman filter, control noise and measurement noise. E is the expected value and assume that the vector dimensions are entirely compatible.
It means u and v are orthogonal. 

If u or v or both have zero mean then they are also uncorrelated. 

If they are uncorrelated and jointly gaussian then they are also independent.