For a real square matrix $M$, Hadamard's inequality gives an upper bound $H$ for the determinant of $M$. This upper bound is sharp if and only if the rows of $M$ are orthogonal. In this paper 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.
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Titolo: | How Tight is Hadamard's Bound? |
Autori: | |
Data di pubblicazione: | 2001 |
Rivista: | |
Abstract: | For a real square matrix $M$, Hadamard's inequality gives an upper bound $H$ for the determinant of $M$. This upper bound is sharp if and only if the rows of $M$ are orthogonal. In this paper 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. |
Handle: | http://hdl.handle.net/11567/508119 |
Appare nelle tipologie: | 01.01 - Articolo su rivista |
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