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<div>In [[mathematics]], two [[real number]]s <math>p, q>1</math> are called '''conjugate indices''' if <br />
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: <math>\frac{1}{p} + \frac{1}{q} = 1.</math> <br />
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Formally, we will also define <math>q = \infty</math> as conjugate to <math>p=1</math> and [[List of Latin phrases: V#vice versa|vice versa]]. <br />
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Conjugate indices are used in [[Hölder's inequality]]. Also, if <math>p, q>1</math> are conjugate indices, the spaces ''L''<sup>''p''</sup> and ''L''<sup>''q''</sup> are [[dual space|dual]] to each other (see [[Lp space|''L''<sup>''p''</sup> space]]). <br />
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==See also==<br />
* [[Beatty's theorem]]<br />
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==References==<br />
* A B Antonevich, ''Linear Functional Equations'', Birkhäuser, 1999. ISBN 3-7643-2931-9.<br />
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{{PlanetMath attribution|id=2051|title=Conjugate index}}<br />
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[[Category:Functional analysis]]</div>213.236.68.144