(Q117184219)

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Hölder's inequality for sums

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Hölder's inequality

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defining formula

|{\boldsymbol {x}}\circ {\boldsymbol {y}}|_{1}\leq |{\boldsymbol {x}}|_{p}|{\boldsymbol {y}}|_{q}

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\sum _{i=1}^{n}x_{i}y_{i}\leq \left(\sum _{i=1}^{n}x_{i}^{p}\right)^{1/p}\left(\sum _{i=1}^{n}y_{i}^{q}\right)^{1/q}

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in defining formula

{\boldsymbol {x}}

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{\boldsymbol {y}}

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\circ

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Hadamard product

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|{\boldsymbol {x}}|_{1}

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|{\boldsymbol {x}}|_{p}

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x_{i}

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Cartesian vector coordinate

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y_{i}

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Cartesian vector coordinate

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n

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dimension of a vector space

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\sum _{i=1}^{n}

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p

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conjugate index

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q

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conjugate index

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maintained by WikiProject

WikiProject Mathematics

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Identifiers

Digital Library of Mathematical Functions ID

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Hölder's_Inequality_for_Sums

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Wikipedia(1 entry)

enwiki Hölder's inequality for sums

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