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).
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