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In recent years two Krylov subspace methods have been proposed for solvingskew symmetric linear systems, one based on the minimum residual condition, theother on the Galerkin condition. We give new, algorithm-independent proofs thatin exact arithmetic the iterates for these methods are identical to theiterates for the conjugate gradient method applied to the normal equations andthe classic Craig's method, respectively, both of which select iterates from aKrylov subspace of lower dimension. More generally, we show that projecting anapproximate solution from the original subspace to the lower-dimensional onecannot increase the norm of the error or residual.

Equivalence of Krylov Subspace Methods for Skew-Symmetric Linear Systems