In the following graph, the diagonal elements in the covariance matrix are the same, which I suppose means the spread of data in either direction should be the same, but why the data points are still more elongated in one direction rather than being a circle?

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#### Best Answer

Diagonal elements are the variances **in the direction of x, y** whereas the eigenvalues are the magnitude of variances **in the direction of the first and second Principal Components**.

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