The maximum determinant of \(\pm 1\) matrices

DOI10.1016/S0024-3795(96)00147-4zbMath0872.15017MaRDI QIDQ1355220

Andrew John Radcliffe, Michael G. Neubauer

Publication date: 9 October 1997

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

zbMATH Keywords

integer matrixmaximum determinantbounds for the determinant\(\pm1\) matrix

Mathematics Subject Classification ID

Determinants, permanents, traces, other special matrix functions (15A15) Miscellaneous inequalities involving matrices (15A45) Matrices of integers (15B36)

Related Items (13)

Classification of small (0, 1) matrices ⋮ A survey of the Hadamard maximal determinant problem ⋮ An inequality for positive definite matrices with applications to combinatorial matrices ⋮ Largest \(j\)-simplices in \(d\)-cubes: Some relatives of the Hadamard maximum determinant problem ⋮ E-optimal and highly E-efficient designs with (mod 4) correlated observations ⋮ Necessary and sufficient conditions in the problem of D-optimal weighing designs with autocorrelated errors ⋮ First order deformations of the Fourier matrix ⋮ D-optimal \((0,1)\)-weighing designs for eight objects ⋮ Computation of Maximal Determinants of Binary Circulant Matrices ⋮ What is known about unit cubes ⋮ D-optimal (0,1)-weighing designs for 10 objects ⋮ Notes on D-optimal designs ⋮ Determinants of certain classes of zero-one matrices with equal line sums

Cites Work

• The maximum determinant of 21\(\times 21\) \((+1,-1)\)-matrices and D-optimal designs
• The exact D-optimal first order saturated design with 17 observations
• D-optimum weighing designs
• Supplementary difference sets and optimal designs
• Determinants of matrices of the conference type
• Theory of optimal designs
• Determinantenabschätzung für binäre Matrizen mit \(n\equiv 3\bmod 4\)
• Determinantenabschätzungen für binäre Matrizen. (Estimation of determinants for binary matrices)
• On Determinants with Elements ±1, II
• On Hadamard's inequality for the determinants of order non-divisible by 4
• A Sequence of (± 1)-Determinants with Large Values
• Determinants with Elements ± 1
• The Hadamard Maximum Determinant Problem
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