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Gram’s Inequality

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Classical and New Inequalities in Analysis

Part of the book series: Mathematics and Its Applications () ((MAEE,volume 61))

Abstract

Let x 1,...,x n be vectors of a unitary space X. Then

$$G\,\left( {{x_1}\,,\,...\,,{x_n}} \right)\, = \,\left[{\begin{array}{*{20}{c}}{\left( {{x_1},\,{x_n}} \right)\,...\,\left( {{x_1}\,,\,{x_n}} \right)} \\ \vdots \\ {\left( {{x_1}\,,\,{x_n}} \right)\,...\,\left( {{x_n}\,,{x_n}} \right)} \end{array}} \right]$$

is called the Gram matrix of the vectors x 1,...,x n .

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Author information

Authors and Affiliations

  1. University of Belgrade, Belgrade, Yugoslavia

    D. S. Mitrinović

  2. University of Zagreb, Zagreb, Croatia

    J. E. Pečarić

  3. Department of Mathematics, Iowa State University of Science and Technology, Ames, Iowa, USA

    A. M. Fink

Authors
  1. D. S. Mitrinović
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  2. J. E. Pečarić
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  3. A. M. Fink
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© 1993 Springer Science+Business Media Dordrecht

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Mitrinović, D.S., Pečarić, J.E., Fink, A.M. (1993). Gram’s Inequality. In: Classical and New Inequalities in Analysis. Mathematics and Its Applications (East European Series), vol 61. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1043-5_20

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  • DOI: https://doi.org/10.1007/978-94-017-1043-5_20

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4225-5

  • Online ISBN: 978-94-017-1043-5

  • eBook Packages: Springer Book Archive

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