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Unformatted text preview: = 0 . But each of these terms is nonnegative, so this is possible if and only if h v,e m +1 i = = h v,e n i = 0 . Finally, using the expression for v given at the beginning, this is possible if and only if v = h v,e 1 i e 1 + + h v,e m i e m . Thus we have shown that k v k 2 = h v,e 1 i 2 + + h v,e m i 2 if and only if v is a linear combination of ( e 1 ,...,e m ), as was to be shown. Date : July 23, 2009....
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 Summer '08
 GUREVITCH
 Math, Vectors

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