Any *M*x*N*-matrix can be decomposed in the following way (Golub and
Van Loan, 1989):

(1) |

When a singular value is zero, the corresponding eigenvector in data (or model) space cannot be mapped into model (or data) space. When a singular value is not zero but is small compared with the largest one (large condition number), the contribution of the corresponding eigenvectors into the solution must be eliminated or attenuated (regularization) because the problem may become unstable.

12/18/1997