It is said that only a linear system of differential equations with all real and complete eigenvalues can be decoupled by applying a spectral decomposition to its coefficient matrix.
Since the singular value decomposition is a generalization of the spectral decomposition, can the SVD be used to decouple linear systems of differential equations with some complex and/or defective eigenvalues?
For defective eigenvalues, what about a spectral decomposition where the leftmost matrix includes generalized eigenvectors?