The maximal determinant and subdeterminants of \(\pm\)1 matrices.

DOI10.1016/S0024-3795(03)00584-6zbMath1048.15008OpenAlexW1976208484MaRDI QIDQ1414147

Tianbing Xia, Christos Koukouvinos, Marilena Mitrouli, Jennifer Seberry Wallis

Publication date: 19 November 2003

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

Full work available at URL: https://doi.org/10.1016/s0024-3795(03)00584-6

zbMATH Keywords

algorithmHadamard matricesdeterminantsminorssubdeterminants\(\pm 1\)-matricescompletely pivoted matrix

Mathematics Subject Classification ID

Combinatorial aspects of matrices (incidence, Hadamard, etc.) (05B20) Determinants, permanents, traces, other special matrix functions (15A15) Numerical computation of determinants (65F40) Matrices of integers (15B36)

Related Items (9)

On the computation of maximum minors of Hadamard matrices ⋮ Embedding and extension properties of Hadamard matrices revisited ⋮ Some remarks on Hadamard matrices ⋮ Hadamard Matrices: Insights into Their Growth Factor and Determinant Computations ⋮ \(D\)-optimal designs embedded in Hadamard matrices and their effect on the pivot patterns ⋮ General lower bounds on maximal determinants of binary matrices ⋮ Determinant evaluations for binary circulant matrices ⋮ Evaluation of minors associated to weighing matrices ⋮ The maximal determinant of cocyclic (-1,1)-matrices over \(D_{2t}\)

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
• An algorithm to find formulae and values of minors for Hadamard matrices. II
• Combinatorics. Room squares, sum-free sets, Hadamard matrices
• Pivot size in Gaussian elimination
• Determinantenabschätzung für binäre Matrizen mit \(n\equiv 3\bmod 4\)
• Determinantenabschätzungen für binäre Matrizen. (Estimation of determinants for binary matrices)
• Growth in Gaussian Elimination
• An Algorithm for the Permanent of Circulant Matrices
• A counterexample to a hadamard matrix pivot conjecture
• On the complete pivoting conjecture for a hadamard matrix of order 12
• On Hadamard's inequality for the determinants of order non-divisible by 4
• An algorithm to find formulae and values of minors for Hadamard matrices
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