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.© BrainMass Inc. brainmass.com March 4, 2021, 5:48 pm ad1c9bdddf
Please see the attached file for the full solution.
Summations are investigated as to whether they define norms. The solution is detailed and well presented. The formulas to define a norm are given.