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In article <24OCT199219173765@rosie.uh.edu> chem86@rosie.uh.edu (91F9843) writes:
>Hello,
>             +
>  Let A and A  denote real rectangular matrix and its pseudo-inverse,
>respectively. The latter can be easily found from
>                      +     T  -1 T
>                     A  = (A A)  A
>               T
>as far as B = A A is nonsingular. My question concerns methods of 
>finding pseudo-inverse in singular B case. In "Generalized Inverses
>of Linear Transformations" by Campbell and Meyer I found algorithm
>which uses singular value decomposition of A. On the other hand, in
>"The Force Concept in Chemistry" another (and probably much simpler)
>idea was presented; namely define the pseudo-inverse in the following
>way :
>                      +      T   -1 T
>                     A  =  (A CA)  A C
>
>                                 T
>where C is any matrix for which A CA is nonsingular. 
>Is there any general method of finding such matrix C ?  Since I am not
>a mathematician, I am also not quite sure that the matrix C always exist.
>I will appreciate any ideas.
>
>Robert Fraczkiewicz
>Department of Chemistry
>University of Houston

When B is singular you essentilally have a divide by zero problem.
This means that their are many posible pseudoinverses such that
		+
       A A = I
Thus, the problem is nonunique and the question is which pseduo inverse
is the "best".  Of course, what is best depends on what your original
problem. It may not matter which pseudoinverse you use or it may matter
a great deal.

Singular value decomposition can be cast into the form you've found that
uses the C matrix.  If you want you can think of singular value
decomposition
as a way to find C.