I am trying to obtain the variance of each attribute given the eigenvalues for each attribute. I know the eigenvalues come from the covariance matrix and that the diagonals of the covariance matrix are the variance of each attribute. I then know that when you diagonalize the covariance matrix you get the eigenvalue in each column which represents the variance.
But how does the eigenvalue itself relate to the variance exactly? Is it possible to take the eigenvalues and convert them back to variances?