Difference between revisions of "Template:AotD"

Revision as of 23:07, 15 December 2007

Cauchy-Schwarz inequality

The Cauchy-Schwarz Inequality (which is known by other names, including Cauchy's Inequality, Schwarz's Inequality, and the Cauchy-Bunyakovsky-Schwarz Inequality) is a well-known inequality with many elegant applications... [more]

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 <blockquote style="display:table;background:#eeeeee;padding:10px;" class="toccolours">
-===[[Rearrangement Inequality]]===
+===[[Cauchy-Schwarz inequality]]===
-The '''Rearrangement Inequality''' states that, if <math>A=\{a_1,a_2,\cdots,a_n\}</math> is a [[permutation]] of a [[finite]] [[set]] (in fact, [[multiset]]) of [[real number]]s and <math>B=\{b_1,b_2,\cdots,b_n\}</math> is a permutation of another finite set of real numbers, the quantity <math>a_1b_1+a_2b_2+\cdots+a_nb_n</math> is maximized when <math>{A}</math> and <math>{B} </math> are similarly sorted (that is, if <math>a_k</math> is greater than or equal to exactly <math>{i}</math> of the other members of <math>A</math>, then <math> {b_k} </math> is also greater than or equal to exactly <math>{i}</math> of the other members of <math>B</math>).  Conversely, <math>a_1b_1+a_2b_2+\cdots+a_nb_n</math> is minimized when <math>A</math> and <math>B</math> are oppositely sorted (that is, if <math>a_k</math> is less than or equal
+The Cauchy-Schwarz Inequality (which is known by other names, including Cauchy's Inequality, Schwarz's Inequality, and the Cauchy-Bunyakovsky-Schwarz Inequality) is a well-known inequality with many elegant applications... [[Cauchy-Schwarz inequality|[more]]]
 </blockquote>

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Difference between revisions of "Template:AotD"

Revision as of 23:07, 15 December 2007

Cauchy-Schwarz inequality