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All vectors are in R^ n. Prove the following statements. a) v·v=||v||2 b) If ||u||2 + ||v||2...

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Basic Math

All vectors are in R^ n. Prove the following statements.

a) v·v=||v||2


b) If ||u||2 + ||v||2 = ||u + v||2, then u and v areorthogonal.

c) (Schwarz inequality) |v · w| ? ||v||||w||.

Answer & Explanation Solved by verified expert
4.0 Ratings (513 Votes)
a Let v v1v2vn Then vv v12v22vn2 v2 b Let u u1u2un and v v1v2vn Then u2 u12u22un2 and v2 v12v22vn2 Further uv u1v1u2v2unvn so that uv2 u1v1 2u2v2 2unvn 2 u12v122    See Answer
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