Linear Algebra and Its Applications · Problem 3.2.7

Orthogonality — Gilbert Strang

Mathematics · cosines-projections-onto-lines

Problem

By choosing the correct vector bb in the Schwarz inequality, prove that (a1+⋯+an)2≤n(a12+⋯+an2).(a_1 + \cdots + a_n)^2 \leq n(a_1^2 + \cdots + a_n^2). When does equality hold?

Browse the problem library