In
mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
, two
real number
In mathematics, a real number is a number that can be used to measure a ''continuous'' one-dimensional quantity such as a distance, duration or temperature. Here, ''continuous'' means that values can have arbitrarily small variations. Every real ...
s
are called conjugate indices (or Hölder conjugates) if
:
Formally, we also define
as conjugate to
and
vice versa
References
Additional references
*
*
{{Latin phrases
V
ca:Locució llatina#V
da:Latinske ord og vendinger#V
fr:Liste de locutions latines#V
id:Daftar frasa Latin#V
it:Locuzioni latine#V
nl:Lijst van Latijnse spreekwoorden en ui ...
.
Conjugate indices are used in
Hölder's inequality. If
are conjugate indices, the spaces ''L''
''p'' and ''L''
''q'' are
dual
Dual or Duals may refer to:
Paired/two things
* Dual (mathematics), a notion of paired concepts that mirror one another
** Dual (category theory), a formalization of mathematical duality
*** see more cases in :Duality theories
* Dual (grammatical ...
to each other (see
''L''''p'' space).
See also
*
Beatty's theorem
References
* Antonevich, A. ''Linear Functional Equations'', Birkhäuser, 1999. .
Functional analysis
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