Covariance and correlation

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Zero Co variance implies zero correlation. But converse is not necessarily true.Can you elaborate this please?

 

[berrymucho]

Zero Co variance implies zero correlation. But converse is not necessarily true.Can you elaborate this please?

Did you mean to ask about the relationship between zero correlation (covariance) and independence instead? Mathematically

Cov(x1,x2) = SD(x1) * SD(x2) * rho_12

So generally if Cov=0 <–> rho=0 and vice versa. And in the case the standard deviation of one of the variable SD(x_i)=0 then Cov(i,j)=0 by construction and rho_12 = 0/0 would be technically undefined. However one would typically see it as undefined meaning ~ zero since no correlation exists when speaking of a constant variable. Hope this helps!