Validity of proof of Cauchy-Schwarz inequality

  • #1
Proof: If either x or y is zero, then the inequality |x · y| ≤ | x | | y | is trivially correct because both sides are zero.
If neither x nor y is zero, then by x · y = | x | | y | cos θ,
|x · y|=| x | | y | cos θ | ≤ | x | | y |
since -1 ≤ cos θ ≤ 1

How valid is this a proof of the Cauchy-Schwarz inequality?
 

Answers and Replies

  • #2
FactChecker
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It looks good as long as x · y = | x | | y | cos θ is given by definition or is already proven. (It's good form to indicate "by definition" or "by Lemma xxx", etc.)
 
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Likes HaniZaheer
  • #3
Alright, thanks a lot
 

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