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The Cauchy-Schwarz inequality : Proofs and applications in various spaces / Cauchy-Schwarz olikhet : Bevis och tillämpningar i olika rum

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.

Identiferoai:union.ndltd.org:UPSALLA1/oai:DiVA.org:kau-38196
Date January 2015
CreatorsWigren, Thomas
PublisherKarlstads universitet, Avdelningen för matematik
Source SetsDiVA Archive at Upsalla University
LanguageEnglish
Detected LanguageEnglish
TypeStudent thesis, info:eu-repo/semantics/bachelorThesis, text
Formatapplication/pdf, application/pdf
Rightsinfo:eu-repo/semantics/openAccess, info:eu-repo/semantics/openAccess

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