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adriank
#17
Nov21-08, 03:39 AM
P: 534
Quote Quote by HallsofIvy View Post
If you add n-k independent vectors to the given k vectors to make a basis for R^n and then apply Gram-Schmidt, the vectors {u_(k+1),..., u_n} are not necessarily orthogonal to the original set of k vectors so does NOT solve the problem.
Why not? The given set of k vectors and the set obtained by applying Gram-Schmidt have the same span.