Suppose that u is a non-zero vector in R^n. Prove that ||u-v|| = ||u|| - ||v|| if and only if v=ku for k element of R with 0 <= k <= 1. I tried putting ku in the equation but seem to have hit a road block any ideas?
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Well if then . For the converse, it depends; is the standard norm in or a norm with respect to an arbitrary inner product? What are you familiar with? You have to be specific.
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