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How Good is Hadamard’s Inequality for Determinants?

Published online by Cambridge University Press:  20 November 2018

John D. Dixon
John D. Dixon*
Affiliation:
Department of Mathematics and Statistics, Carleton University, Ottawa, CanadaK1S 5B6
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Abstract

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Let A be a real n × n matrix and define the Hadamard ratio h(A) to be the absolute value of det A divided by the product of the Euclidean norms of the columns of A. It is shown that if A is a random variable whose distribution satisfies some simple symmetry properties then the random variable log h(A) has mean and variance . In particular, for each ε > 0, the probability that h(A) lies in the range tends to 1 as n tends to ∞.

Keywords

15A1560D05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 27 , Issue 3 , 01 September 1984 , pp. 260 - 264
Copyright
Copyright © Canadian Mathematical Society 1984

References

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