- Experiment. Math.
- Volume 10, Issue 3 (2001), 331-336.
How Tight is Hadamard's Bound?
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.
Experiment. Math., Volume 10, Issue 3 (2001), 331-336.
First available in Project Euclid: 25 November 2003
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Abbott, John; Mulders, Thom. How Tight is Hadamard's Bound?. Experiment. Math. 10 (2001), no. 3, 331--336. https://projecteuclid.org/euclid.em/1069786341