  Many numerical problems with input $x$ and output $y$ can be formulated as an
system of equations $F(x, y) = 0$ where the goal is to solve for $y$. The
condition number measures the change of $y$ for small perturbations to $x$.
From this numerical problem, one can derive a (typically underdetermined)
subproblem by omitting any number of constraints from $F$. We propose a
condition number for underdetermined systems that relates the condition number
of a numerical problem to those of its subproblems. We illustrate the use of
our technique by computing the condition of two problems that do not have a
finite condition number in the classic sense: any two-factor matrix
decompositions and Tucker decompositions.
