Use of covariance matrix and how sigma xy = 0 is interpreted
Needs more understanding on covariance matrix
Hello @komal4282,
In probability theory and statistics, covariance is a measure of the joint variability of two random variables. If the greater values of one variable mainly correspond with the greater values of the other variable, and the same holds for the lesser values, (i.e., the variables tend to show similar behavior), the covariance is positive. In the opposite case, when the greater values of one variable mainly correspond to the lesser values of the other, (i.e., the variables tend to show opposite behavior), the covariance is negative. The sign of the covariance therefore shows the tendency in the linear relationship between the variables.
A covariance matrix is a matrix that has covariances of random variables as elements.
cov(x, y) = [[cov(x, x) , cov(x, y)],
[cov(y, x), cov(y, y)]]
Also, cov(x, x) is nothing but var(x) and similarly cov(y, y) is var(y).
Now cov(x, y) = 0 means there is no linear relationship between the two variables x & y. They are uncorrelated.
To get an understanding, try plotting the samples from a multivariate distribution with different values of covariance matrix.
Happy Learning 
Thanks
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