Symmetric and Skew-Symmetric {0,±1}-Matrices with Large Determinants

Gary R. W. Greaves, Sho Suda

Type: Article

Publication Date: 2017-07-13

Citations: 15

DOI: https://doi.org/10.1002/jcd.21567

Abstract

We show that the existence of -matrices having largest possible determinant is equivalent to the existence of certain tournament matrices. In particular, we prove a recent conjecture of Armario. We also show that large submatrices of conference matrices are determined by their spectrum.

Locations

arXiv (Cornell University) - View - PDF
DR-NTU (Nanyang Technological University) - View - PDF
DataCite API - View
Journal of Combinatorial Designs - View

Similar Works

Action	Title	Year	Authors
+ PDF Chat	On (−1, 1)-Matrices of Skew Type with the Maximal Determinant and Tournaments	2015	José Ándrés Armario
+ PDF Chat	The maximal determinant and subdeterminants of ±1 matrices	2003	Jennifer Seberry Tianbing Xia Christos Koukouvinos Marilena Mitrouli
+	Digraphs and eigenvalues of (0,1)-matrices	2011	Richard Brualdi
+ PDF Chat	Tournament matrices with extremal spectral properties	1994	Stephen Kirkland Bryan L. Shader
+	Square (1,−1)-matrices with large determinants and near-Hadamard matrices	2022	Koji Momihara Sho Suda Qing Xiang
+	A family of nonnegative matrices with prescribed spectrum and elementary divisors	2016	Ricardo L. Soto Elvis Valero
+	Characterizations of matrices for which certain determinantal equalities hold	1969	Beryl Manfield Green
+	Classification de certaines matrices 0–1	1977	J.D. MacAllister Michel Sakarovitch
+	Spectral Radius of Non-negative Matrices and Digraphs	2002	Xiao Dong Zhang Jiong Sheng Li
+	{0,1} Completely positive matrices	2004	Abraham Berman Changqing Xu
+	0-1 matrices whose squares have bounded entries	2020	Zhenhua Lyu
+	Bruhat order for symmetric (0,1)-matrices	2017	Susana Furtado
+	A characterization of skew Hadamard matrices and doubly regular tournaments	2012	Hiroshi Nozaki Sho Suda
+	Non-negative Matrices and Digraphs	2009	Abraham Berman Naomi Shaked-Monderer
+	Non-negative Matrices and Digraphs	2011	Abraham Berman Naomi Shaked-Monderer
+	Non-negative Matrices and Digraphs	2011	Abraham Berman Naomi Shaked-Monderer
+	0-1 matrices with zero trace whose squares are 0-1 matrices	2018	Zejun Huang Zhenhua Lyu
+	Spectral Radius of Nonnegative Matrices and Digraphs	2005	Jiong Zhang
+	Doubly regular tournaments are equivalent to skew hadamard matrices	1972	K. B. Reid Ezra Brown
+	Determinant and eigenvalue inequalities involving nonnegative matrices	2023	Rajesh Sharma Manish Pal Anjana Sharma

Works That Cite This (13)

Action	Title	Year	Authors
+	Spectral symmetry in conference matrices	2020	Willem H. Haemers Leila Parsaei Majd
+	Matricial characterization of tournaments with maximum number of diamonds	2019	Wiam Belkouche Abderrahim Boussaïri Soufiane Lakhlifi Mohamed Zaidi
+	Equiangular lines and the Lemmens–Seidel conjecture	2019	Yen-chi Roger Lin Wei-Hsuan Yu
+ PDF Chat	Spectral symmetry in conference matrices	2021	Willem H. Haemers Leila Parsaei Majd
+	An exact extremal result for tournaments and 4-uniform hypergraphs	2018	Wiam Belkouche Abderrahim Boussaïri Soufiane Lakhlifi Mohammed Zaidi
+ PDF Chat	Signed (0,2)‐graphs with few eigenvalues and a symmetric spectrum	2022	Gary R. W. Greaves Zoran Stanić
+	Equiangular lines and the Lemmens-Seidel conjecture	2018	Yen-chi Roger Lin Wei-Hsuan Yu
+	Partitions of Equiangular Tight Frames	2016	James Rosado Hiêú D. Nguyêñ Lei Cao
+ PDF Chat	On the Smith normal form of skew E-W matrices	2016	José Ándrés Armario
+	Characterization of k-spectrally monomorphic two-graphs	2024	Abderrahim Boussaïri Imane Souktani Mohamed Zouagui

Works Cited by This (12)

Action	Title	Year	Authors
+ PDF Chat	On Hadamard's inequality for the determinants of order non-divisible by 4	1964	Mieczyslaw Wojtas
+	Equiangular lines in Euclidean spaces	2015	Gary R. W. Greaves Jack H. Koolen Akihiro Munemasa Ferenc Szöllősi
+ PDF Chat	Tournament matrices with extremal spectral properties	1994	Stephen Kirkland Bryan L. Shader
+ PDF Chat	A characterization of skew Hadamard matrices and doubly regular tournaments	2012	Hiroshi Nozaki Sho Suda
+	Doubly regular tournaments are equivalent to skew hadamard matrices	1972	K. B. Reid Ezra Brown
+ PDF Chat	The main eigenvalues of a graph: A survey	2007	Peter Rowlinson
+	An eigenvalue approach evaluating minors for weighing matrices <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mrow><mml:mi>W</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>n</mml:mi><mml:mtext>,</mml:mtext><mml:mi>n</mml:mi><mml:mo>-</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math>	2011	Anna Karapiperi Marilena Mitrouli Michael Neubauer Jennifer Seberry
+	Algebraic multiplicity of the eigenvalues of a tournament matrix	1992	D. de Caen David A. Gregory Steve Kirkland Norman J. Pullman John S. Maybee
+	Spectra of Graphs	2011	Andries E. Brouwer Willem H. Haemers
+	A very short proof of Cauchy's interlace theorem for eigenvalues of Hermitian matrices	2005	Steve Fisk