Generalized Inverses and Underdetermined Systems

Hi,

Suppose you have an underdetermined system of linear equations (so
number of eqns < number of vars), which can be solved. Normally, of
course, such a system produces an infinite number of solutions which
can be written in a parametrized form.

Recently, I was reading a book where the author used the Moore-Penrose
inverse to solve an undetermined system of linear equations. I know
that it can be used to solve such a system, but I am wondering why one
would want to use it. I'm used to seeing the MP inverse for the
solution of least-squares problems where the system is overdetermined
instead of undetermined. Here you'd use the MP inverse because it
minimizes the residual of interest, but for an underdetermined system,
the residual should be zero, since a solution does exist. Does this
approach minimize another norm (such as that of the solution set)?

TIA,

Juno

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