How tight is Hadamard’s bound? (English) Zbl 0992.15005

Formulas are derived for the values and variances of \(|d |/H\) and of \(\log (|d|/H)\) for a random matrix \(M\), where \(H\) is Hadamard bound for \(M\) and \(d\) is the determinant. Asymptotic expansions are also given in terms of the matrix dimension \(n\). These results improve the bounds given by J. Abbott et al. [Proc. 1999 International Symposium on Symbolic and Algebraic Computation New York (1999)].


15A15 Determinants, permanents, traces, other special matrix functions
15A45 Miscellaneous inequalities involving matrices
15B52 Random matrices (algebraic aspects)


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