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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[1] 1. Cabay, S. and Lam, T. P. L., Congruence techniques for the exact solution of integer systems of linear equations, ACM Trans. Math. Software 3 (1977) 386–397. Google Scholar

[2] 2. Dixon, J. D., Estimating extremal eigenvalues and condition numbers of matrices, SIAM J. Numer. Anal., 20 (1983), 812–814. Google Scholar

[3] 3. Johnson, C. R. and Newman, M., How bad is the Hadamard determinantal bound?, J. Res. Nat. Bureau Stand. 78B (1974) 167–169. Google Scholar

[4] 4. Shiue, J. S., On a generalization of a theorem of Johnson and Newman, Soochow J. Math. Natur. Sci. 2 (1976) 57–61. Google Scholar

[5] 5. Szekeres, G., The average value of skew Hadamard matrices, in Proc. First Austral. Conf. Combinatorial Math. (Newcastle, 1972), pp. 55–59. Google Scholar

[6] 6. Szekeres, G. and Turán, P., On an extremal problem in determinant theory, Mat. természett. Ertes. 56 (1937) 796–804 (Hungarian) (see Zbl. Math. 18 (1938) 387). Google Scholar

[7] 7. Wilks, S. S., Mathematical Statistics, Wiley, New York, 1962. Google Scholar

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