A sharp inequality for vector norms
TrifTiberiu · Octogon Mathematical Magazine archive · 2002
We prove that for all vectors a1,..., an ∈ Rm it holds that ||a1|| +...+||an|| ≤ ||a1 +...+an|| + 2/n Σ1≤i<j≤n||ai-aj||. Moreover, this inequality is sharp in the sense that the factor 2/n cannot b...