Linear Algebra : Norms

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
https://brainmass.com/math/linear-algebra/linear-algebra-norms-11651

Please see the attached file for the full solution.

Thanks ...

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

$2.19