Thread: covariance matrix

Is this right? the reason why the covariance matrix is important is because it allows you to see if 2 variables are independent? because covariance zero means independence?

Independence implies that the covariance is 0.
Not the other way around, UNLESS you have a joint normal distribution.
The covariance or dispersion matrix also gives you the variances along the diagonal.
And you can compare the covariances with those variances to obtain the correlation between random variables.
That shows how related, the rvs are.