(a) Vector norms in our text are equivalent, that is, they are related by double inequalities; for instance, (a) xx ≦x1 ≦n[x]∞ (b) .(1)/(n)|x||1 ≤|x|=≤|| x||1 Hence if for some x, One norm is large (or small), the other norm must also be large (or small). Thus in many investigations the particular choice of a norm is not essential. Prove (18). (b) The Cauchy-Schwarz inequality is |𝐱^⊤ 𝐲| ≤[𝐱]2𝐲2 It is very important. (Proof in Ref. IGR7) listod in App. 1.2 Use it to prove x2 ≤x2 ≤√(n)x2 .(
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