Let x = (x1,..., xn) and y = (y1,..., yn) be any vectors in Rn and, for i = 1,..., n
Chapter 4, Problem 45(choose chapter or problem)
Let x = (x1,..., xn) and y = (y1,..., yn) be any vectors in Rn and, for i = 1,..., n, set ui = xi !"n i=1 x 2 i and vi = yi !"n i=1 y2 i . (a) Show that u = (u1,..., un) and v = (v1,...,vn) lie on the unit hypersphere in Rn. (b) Use the result of Exercise 44 to establish the CauchySchwarz inequality |x y|x y.
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