I feel confused about this paragraph. What does $|x-y|$ mean here? Taking every element of a vector positive? Or length of a vector? I feel so confused. Thanks!
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It's the length of the vector $x-y$. You can see this in the line that follows: $$ x-y=\sqrt{(x-y)\cdot(x-y)}=\sqrt{x\cdot x+y\cdot y-2x\cdot y}=\sqrt{|x|^2+|y|^2-2x\cdot y}. $$
Kim Jong Un
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I updated the question. Can you help me see why we can get derivative with respect to length? – Oct 04 '14 at 16:55
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It is the equation (2.25) – Oct 04 '14 at 16:56
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Can you help me with how to do the "direct calculation" to get (2.25)? – Oct 04 '14 at 16:56