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

Abbott, John; Mulders, Thom

Exp. Math. 10, No. 3, 331-336 (2001).

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)].

Reviewer: Václav Burjan (Praha)

MSC:

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

Keywords:

determinants; Hadamard’s inequality; random matrices; asymptotic expansions

Software:

Hull

References:

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