How many proofs of the Cauchy-Schwarz inequality are there? Is there some kind of reference that lists all of these proofs?
Proofs of the Cauchy-Schwarz Inequality?
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real-analysis
inequality
big-list
inner-product-space
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0I've slightly edited the body your question in order to make it self-contained. I've also added the `real-analysis` tag. – 2011-02-24
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14I would try the book "The Cauchy-Schwarz Masterclass". – 2011-02-24
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0@user3533: excellent. I got that book. It seems that this textbooks also talks about few other inequalities that I was going to study. Do you know any other references that basically is about different kind of inequalities and their proofs? Thanks – 2011-02-24
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2@Vafa: many Olympiad preparation books include sections on inequalities. There is also Kedlaya's notes: http://www.artofproblemsolving.com/Resources/Papers/KedlayaInequalities.pdf – 2011-02-24
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0Found Inequalities By Hardy, too: http://www.amazon.com/Inequalities-Cambridge-Mathematical-Library-Hardy/dp/0521358809 – 2011-02-24
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3Your first question is essentially unanswerable, except, maybe, by "many"... – 2011-02-24
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0@Vafa Khalighi: It is Hardy, Littlewood (Author) and Pólya. – 2011-03-01
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0@Vafa Khalighi: Here is a link that gives 12 different proofs of the Cauchy-Schwarz that may be of interest to you. http://ajmaa.org/RGMIA/papers/v12e/Cauchy-Schwarzinequality.pdf – 2012-07-02