Use the Cauchy Schwarz inequality in an inner product space to show that (a) If u 1, then (u,v)2 v 2 for all v in V (b) (x cos y sin) y2 x2 y2 for all real x,y, and (c) r1v1 rnvn 2 r1 rn v 2 for all vectors v and all r, 0 in R ...

b If u cos 0 sin 0 in R 2 with th ...

Use the Cauchy-Schwarz inequality in an inner product space to show that: (a) If | u ||

Question:

Use the Cauchy-Schwarz inequality in an inner product space to show that:
(a) If | u || < 1, then (u,v)2 < ||v||2 for all v in V.
(b) (x cosθ + y sinθ) y2 < x2 + y2 for all real x,y, and θ.
(c) ||r1v1 + - + rnvn||2 < [r1 ||+ - + rn|| v||]2 for all vectors v" and all r, > 0 in R.