Geodesic
How Good is Hadamard’s Inequality for Determinants?
Canadian mathematical bulletin, Tome 27 (1984) no. 3, pp. 260-264

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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 ∞.
DOI : 10.4153/CMB-1984-039-2
Mots-clés : 15A15, 60D05 
Dixon, John D. How Good is Hadamard’s Inequality for Determinants?. Canadian mathematical bulletin, Tome 27 (1984) no. 3, pp. 260-264. doi: 10.4153/CMB-1984-039-2
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     author = {Dixon, John D.},
     title = {How {Good} is {Hadamard{\textquoteright}s} {Inequality} for {Determinants?}},
     journal = {Canadian mathematical bulletin},
     pages = {260--264},
     year = {1984},
     volume = {27},
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     doi = {10.4153/CMB-1984-039-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1984-039-2/}
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