The Cauchy–Schwarz Inequality

Simo Puntanen (), George P. H. Styan () and Jarkko Isotalo ()
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Simo Puntanen: University of Tampere, School of Information Sciences
George P. H. Styan: McGill University, Department of Mathematics & Statistics
Jarkko Isotalo: University of Tampere, School of Information Sciences

Chapter Chapter 20 in Matrix Tricks for Linear Statistical Models, 2011, pp 415-426 from Springer

Abstract: Abstract As Steele (2004, p. 1) says, there is no doubt that the Cauchy–Schwarz inequality is one of the most widely and most important inequalities in all of mathematics. This chapter gives some examples of its use in statistics; further examples appear in several places in this book. The Cauchy–Schwarz inequality is also known as the Cauchy–Bouniakowsky–Schwarz inequality and is named after Augustin-Louis Cauchy (1789–1857) (see also Philatelic Item 12.1, p. 290), Viktor Yakovlevich Bouniakowsky [Buniakovskii, Bunyakovsky] (1804–1899), and [Karl] Hermann Amandus Schwarz (1843–1921); see Cauchy (1821)1 Bouniakowsky (1859, pp. 3–4), and Schwarz (1888, pp. 343–345), and the book by Steele (2004, Ch. 1).

Keywords: Form Versus; Matrix Version; Schwarz Inequality; Full Column Rank; Column Space (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-10473-2_21

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DOI: 10.1007/978-3-642-10473-2_21

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