  In recent years two Krylov subspace methods have been proposed for solving
skew symmetric linear systems, one based on the minimum residual condition, the
other on the Galerkin condition. We give new, algorithm-independent proofs that
in exact arithmetic the iterates for these methods are identical to the
iterates for the conjugate gradient method applied to the normal equations and
the classic Craig's method, respectively, both of which select iterates from a
Krylov subspace of lower dimension. More generally, we show that projecting an
approximate solution from the original subspace to the lower-dimensional one
cannot increase the norm of the error or residual.
