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On Eutactic Forms

Published online by Cambridge University Press:  20 November 2018

Avner Ash
Avner Ash*
Affiliation:
Columbia University, New York, New York
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Let (aij) = A be a positive definite n × n symmetric matrix with real entries. To it corresponds a positive definite quadratic form ƒ on Rn: ƒ(x) = txAx = ∑ aijXiXj for x any column vector in Rn. The set of values ƒ(y) for y in Zn — {0} has a minimum m (A) > 0 and the number of “minimal vectors“ y1, … , yr in Zn for which ƒ(yi) = m (A) is finite. By definition, ƒ and A are called eutactic if and only if there are positive numbers s1 ,… , sr such that

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 5 , 01 October 1977 , pp. 1040 - 1054
Copyright
Copyright © Canadian Mathematical Society 1977

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