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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.

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

Wigren, Thomas January 2015 (has links)
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.
Cauchy-Schwarz inequality
mathematical induction
triangle inequality
Pythagorean theorem
arithmetic-geometric means inequality
inner product space
Mathematical Analysis
Matematisk analys

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