How to calculate the covariance matrix

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I tried searching a lot on the net and got the following sources:

Source One

Source Two

The first source seems to be incorrect cause when I calculate it using matlab it comes to be different from what they have given as the answer. As for the second link I cant understand that cause its not completely explaining as to how to calculate. Could anyone please provide me with a sound link or explain how to calculate a co-variance matrix?

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1 Answer

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I finally understood the concept behind co-variance. Co-variance is different for population data and sample data.

Following is the method I followed:

Let $A$ be a $n \times m$ matrix where $n$ is the number of rows (observations) and $m$ represents the number of columns (variables).
Let $\mathbf e$ be the $n \times 1$ column vector composed entirely of ones. Then,$$ X= A - \left(\frac{1}{n}\right)\mathbf e\mathbf e^TA $$Then, denote$$ Y = X^TX. $$

Next is the step that differs for population data and sample data.

In case of population data, the covariance matrix $\Sigma$ is given by :$$ \Sigma=\left(\frac{1}{n}\right)Y $$
and in case of sample data, the covariance matrix $\Sigma$ is given by :$$ \Sigma=\left(\frac{1}{n-1}\right)Y $$Hope it helps anyone stuck on a similar problem.

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