"Generalized inverses are useful in formulating theoretical statements as those above, ut, just as in the case of the ordinary inverse, generalized inverses are not practical computational tools. In addition to being computationally inefficient, serious numerical problems result from the fact that A+ needs not be a continuous function of the entries of A. ... Not only is A+(x) discontinuous in the sense that lim_{x->0}A+(x)!=A+(0), but it is discontinuous in the worst way because as A(x) comes closer to A(0) the matrix A+(x) moves farther away from A+(0)."
Here A+ denotes Moore-Penrose pseudo-inverse and A(x) = [1, 0; 0, x] in Matlab notation (or Numpy? I am very rusty on Matlab). And in case you are wondering why the generalized inverse is plural, there are different kinds of generalized inverses, Drazin inverse being a well defined alternative.