Experimental Mathematics

How Tight is Hadamard's Bound?

John Abbott and Thom Mulders

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Abstract

For a real square matrix $M$, Hadamard's inequality gives an upper bound $H$ for the determinant of $M$; the bound is sharp if and only if the rows of $M$ are orthogonal. We study how much we can expect that $H$ overshoots the determinant of $M$, when the rows of $M$ are chosen randomly on the surface of the sphere. This gives an indication of the "wasted effort'' in some modular algorithms.

Article information

Source
Experiment. Math., Volume 10, Issue 3 (2001), 331-336.

Dates
First available in Project Euclid: 25 November 2003

Permanent link to this document
https://projecteuclid.org/euclid.em/1069786341

Mathematical Reviews number (MathSciNet)
MR1917421

Zentralblatt MATH identifier
0992.15005

Subjects
Primary: 15A15: Determinants, permanents, other special matrix functions [See also 19B10, 19B14]

Citation

Abbott, John; Mulders, Thom. How Tight is Hadamard's Bound?. Experiment. Math. 10 (2001), no. 3, 331--336. https://projecteuclid.org/euclid.em/1069786341


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