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In Praise of the Gram Matrix

In: The Mathematics of Paul Erdős I

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  • Moshe Rosenfeld

    (Pacific Lutheran University, Department of Computer Science)

Abstract

Summary We use the Gram matrix to prove that the largest number of points in R d such that the distance between all pairs is an odd integer (the square root of an odd integer) is ≤ d + 2 and we characterize all dimensions d for which the upper bound is attained. We also use the Gram matrix to obtain an upper bound for the smallest angle determined by sets of n lines through the origin in R d .

Suggested Citation

  • Moshe Rosenfeld, 2013. "In Praise of the Gram Matrix," Springer Books, in: Ronald L. Graham & Jaroslav Nešetřil & Steve Butler (ed.), The Mathematics of Paul Erdős I, edition 2, pages 551-557, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4614-7258-2_35
    DOI: 10.1007/978-1-4614-7258-2_35
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