  This paper establishes a variant of Stewart's theorem (Theorem~6.4 of
Stewart, {\em SIAM Rev.}, 15:727--764, 1973) for the singular subspaces
associated with the SVD of a matrix subject to perturbations. Stewart's
original version uses both the Frobenius and spectral norms, whereas the new
variant uses the spectral norm and any unitarily invariant norm that offer
choices per convenience of particular applications and lead to sharper bounds
than that straightforwardly derived from Stewart's original theorem with the
help of the well-known equivalence inequalities between matrix norms. Of
interest in their own right, bounds on the solution to two couple Sylvester
equations are established for a few different circumstances.
