  Solving a singular linear system for an individual vector solution is an
ill-posed problem with a condition number infinity. From an alternative
perspective, however, the general solution of a singular system is of a bounded
sensitivity as a unique element in an affine Grassmannian. If a singular linear
system is given through empirical data that are sufficiently accurate with a
tight error bound, a properly formulated general numerical solution uniquely
exists in the same affine Grassmannian, enjoys Lipschitz continuity and
approximates the underlying exact solution with an accuracy in the same order
as the data. Furthermore, any backward accurate numerical solution vector is an
accurate approximation to one of the solutions of the underlying singular
system.
