In article <fnSfirstname.lastname@example.org>, Richard Hayden <email@example.com> wrote:
> Hi, > > This seems to me that it should be trivial but I am having trouble > proving it. > > Let A be an n x n real matrix and let S be a closed subset of R^n. > Assume that y \in S is the unique solution in S of Ay = 0. > > Then if A x_n -> 0 as n -> \infty for x_n \in S, does it hold that x_n > -> y as n -> \infty? > > Would be grateful for any assistance. > > Thanks, > > Richard.
Perhaps you would like to assume S is closed and convex?