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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.

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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.

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