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    Linear Algebra : Norms

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    For any x=(x1,....,xn), let us try to define a norm two ways. Consider

    (a) ||X||1=summation |Xi| from i=1 to n

    (b) ||X||b=summation |xi-xj| from i,j=1 to n

    Does either one of these formulas define a norm? If yes, show that all three axioms of norm hold. If no, demonstrate which axiom fails.

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    Solution Summary

    Summations are investigated as to whether they define norms. The solution is detailed and well presented. The formulas to define a norm are given.