SOLUTION: Let u, v ∈ R^n be vectors in R^n (a) State and prove the Cauchy - Schwarz inequality. Give a necessary and sufficient condition on u, v ∈ R^n such that the equality holds.

Algebra ->  Vectors -> SOLUTION: Let u, v ∈ R^n be vectors in R^n (a) State and prove the Cauchy - Schwarz inequality. Give a necessary and sufficient condition on u, v ∈ R^n such that the equality holds.       Log On


   



Question 1203667: Let u, v ∈ R^n be vectors in R^n
(a) State and prove the Cauchy - Schwarz inequality. Give a necessary and sufficient
condition on u, v ∈ R^n such that the equality holds.
(b) State and prove the triangle inequality. Show that the equality holds if and only if u is a scalar multiple of v.

Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
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For (a), see the proof under this link

https://dept.math.lsa.umich.edu/~speyer/417/CauchySchwartz.pdf