## Experimental Mathematics

### How Tight is Hadamard's Bound?

#### 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