What type of singularity? Are you referring to some eigenvalues being zero? Then you can in some circumstances work with a regularisation in which you add a small positive number to all the diagonal elements - this has the effect that the matrix may become positive definite (if the eigenvalues already in the original matrix were >= 0). If you then re-run whatever program you are using, and repeatedly lower those diagonal values towards zero, you will see whether something you are looking at converges (in which case you have solved the problem) or if something tends to infinity (in which case you probably have failed). :-)

thank you Michael, i'm working with the eigenvalues matrix, i need to calculate her inverse but she has a determinant of zero, so i thaught maybe there's some mathematical ways to ajust that. i will try your advise.

You can also take a look at the pseudo-inverse

A trick similar to Michael's one:

Laplacian matrix L of an electrical network has one zero eigenvalue. To overpass the obstacle, WU, F. Y. in his paper  Theory of Resistor Networks: the Two-Point Resistance, J. Phys. A: Mathematical and General 37 (2004), 6653–73 added a small h-multiple of L to the Laplacian. The eigenvalues of L+hL are shifted, the eigenvectors are the same as those of L.

We used and explained this trick in our paper for non-symetric matrices in http://iris.elf.stuba.sk/JEEEC/data/pdf/5_114-04.pdf

Dear Tarif,

Please see the attached file.

thank you all to your responses they was really helpfull, and i managed to ''get rid '' of the singularity.