  By singular value decomposition (SVD) of a numerically singular Hessian
matrix and a numerically singular system of linear equations for the
experimental data (accumulated in the respective ${\chi ^2}$ function) and
constraints, least square solutions and their propagated errors for the
non-parametric extraction of Partons from $F_2$ are obtained.
  SVD and its physical application is phenomenologically described in the two
cases. Among the subjects covered are: identification and properties of the
boundary between the two subsets of ordered eigenvalues corresponding to range
and null space, and the eigenvalue structure of the null space of the singular
matrix, including a second boundary separating the smallest eigenvalues of
essentially no information, in a particular case. The eigenvector-eigenvalue
structure of "redundancy and smallness" of the errors of two pdf sets, in our
simplified Hessian model, is described by a secondary manifestation of deeper
null space, in the context of SVD.
