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The Cauchy-Schwarz inequality: Proofs and applications in various spaces
Karlstad University, Faculty of Technology and Science, Department of Mathematics.
2015 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesisAlternative title
Cauchy-Schwarz olikhet : Bevis och tillämpningar i olika rum (Swedish)
Abstract [en]

We give some background information about the Cauchy-Schwarz inequality including its history. We then continue by providing a number of proofs for the inequality in its classical form using various proof techniques, including proofs without words. Next we build up the theory of inner product spaces from metric and normed spaces and show applications of the Cauchy-Schwarz inequality in each content, including the triangle inequality, Minkowski's inequality and Hölder's inequality. In the final part we present a few problems with solutions, some proved by the author and some by others.

Place, publisher, year, edition, pages
2015. , 35 p.
Keyword [en]
Cauchy-Schwarz inequality, mathematical induction, triangle inequality, Pythagorean theorem, arithmetic-geometric means inequality, inner product space
National Category
Mathematical Analysis
URN: urn:nbn:se:kau:diva-38196OAI: diva2:861242
Subject / course
Available from: 2016-02-05 Created: 2015-10-15 Last updated: 2016-02-05Bibliographically approved

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Department of Mathematics
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