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I Validity of proof of Cauchy-Schwarz inequality

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  1. Nov 23, 2016 #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?
     
  2. jcsd
  3. Nov 23, 2016 #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.)
     
  4. Nov 24, 2016 #3
    Alright, thanks a lot
     
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