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.

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) (Show Source): You can put this solution on YOUR website!
.

For (a), see the proof under this link

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

RELATED QUESTIONS
u=(4,1,1) and v=(2,-1,3) verify the cauchy schwarz inequallity... (answered by ikleyn)

hello pleases can you help me with this question. Let u and v be non-zero vectors in R3... (answered by ikleyn)

Let u and v be non-zero vectors in R^3 in standard position. Prove that if u and v are of (answered by ikleyn)

Let u and v be non-zero vectors in R^3 in standard position. Prove that if u and v are of (answered by greenestamps)

Let T, U: V to W be linear transformations. Prove that: a. R(T+U) is a subset of... (answered by khwang)

1)u�u>=0 and u�u=0 if and only if u=0 prove theorem? 2)Show that there are no vectors u... (answered by lynnlo)

Please help me ㅠㅠ help me 1)u�u>=0 and u�u=0 if and only if u=0 prove... (answered by lynnlo)

1)u�u>=0 and u�u=0 if and only if u=0 prove theorem? 2)Show that there are no vectors u... (answered by lynnlo)

Q−4: [6+4 marks] Let S={v_1,v_2,v_3} be a linearly independent set of vectors in〖... (answered by CPhill)