Mercer's theorem
In mathematics, specifically functional analysis, Mercer's theorem is a representation of a symmetric positive-definite function on a square as a sum of a convergent sequence of product functions. This theorem, presented in , is one of the most notable results of the work of James Mercer (1883–1932). It is an important theoretical tool in the theory of integral equations; it is used in the Hilbert space theory of stochastic processes, for example the Karhunen–Loève theorem; and it is also used to characterize a symmetric positive semi-definite kernel.
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Axis–angle representationBag-of-words model in computer visionCompact operator on Hilbert spaceEmpirical orthogonal functionsFunctional data analysisGram matrixInner product spaceIsomapJames Mercer (mathematician)Jovan KaramataKarhunen–Loève theoremKernel methodKernel perceptronList of University of Manchester peopleList of functional analysis topicsList of theoremsMercerMercer's conditionMercer's theoremMercer TheoremMercer conditionMercer theoremMercers theoremRegularized least squaresRepresenter theoremReproducing kernel Hilbert spaceSemi-definite kernelString kernel
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Mercer's theorem
In mathematics, specifically functional analysis, Mercer's theorem is a representation of a symmetric positive-definite function on a square as a sum of a convergent sequence of product functions. This theorem, presented in , is one of the most notable results of the work of James Mercer (1883–1932). It is an important theoretical tool in the theory of integral equations; it is used in the Hilbert space theory of stochastic processes, for example the Karhunen–Loève theorem; and it is also used to characterize a symmetric positive semi-definite kernel.
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En mathématiques et plus préci ...... ransformée de Karhunen-Loève).
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In mathematics, specifically f ...... positive semi-definite kernel.
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p/m063440
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Mercer theorem
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En mathématiques et plus préci ...... ransformée de Karhunen-Loève).
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In mathematics, specifically f ...... positive semi-definite kernel.
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Mercer's theorem
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Satz von Mercer
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Théorème de Mercer
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