Is it true that for a square symmetric matrix such as the covariance matrix, the singular values are equal to the eigenvalues? The eigen decomposition for covariance is the same as singular value decomposition?
For a real symmetric positive semi-definite matrix like a covariance matrix, the nonnegative square roots of the eigenvalues are equal to the singular values. The eigenvectors are also equal to the left and right singular vectors. This is because, for these types of matrices, the eigendecomposition and the SVD give equivalent decompositions.
Detailed discussions and derivations can be found in this extensive Mathematics Stack Exchange Question: Intuitively, what is the difference between Eigendecomposition and Singular Value Decomposition?