Singular value decomposition

• What Is the Relationship Between Eigendecomposition and SVD?
  The SVD is linked to the eigendecompositions of A* A and A A*: their eigenvectors give singular vectors and their eigenvalues are squared singular values.
• What Is the Intuitive Relationship Between SVD and PCA?
  For a centered data matrix, PCA directions are the right singular vectors of its SVD; squared singular values give component variances.