Tournament matrices with extremal spectral properties

DOI10.1016/0024-3795(94)90312-3zbMath0790.15021OpenAlexW1984510818MaRDI QIDQ1316183

Bryan L. Shader, Stephen J. Kirkland

Publication date: 20 June 1994

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

Full work available at URL: http://purl.umn.edu/2143

zbMATH Keywords

eigenvaluesPerron vectorskew-Hadamard matrixtournament matrixdoubly regularwalk polynomialwalk space

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Eigenvalues, singular values, and eigenvectors (15A18) Hermitian, skew-Hermitian, and related matrices (15B57)

Related Items

Normal matrices and their principal submatrices of co-order one ⋮ Pseudo-Tournament Matrices and Their Eigenvalues ⋮ Some results on h-hypertournament matrices ⋮ A characterization of skew Hadamard matrices and doubly regular tournaments ⋮ On almost regular tournament matrices ⋮ Uniform sampling ofk-hypertournaments ⋮ Spectra of digraphs ⋮ On the location of the spectrum of hypertournament matrices ⋮ Pick's inequality and tournaments ⋮ Spectral radii of tournament matrices whose graphs are related by an arc reversal ⋮ Some properties complementary to Brualdi-Li matrices ⋮ The spectrum and eigenvectors of the Laplacian matrices of the Brualdi-Li tournament digraphs

Cites Work

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• On tournament matrices
• Algebraic multiplicity of the eigenvalues of a tournament matrix
• Pick's inequality and tournaments
• Doubly regular tournaments are equivalent to skew Hadamard matrices
• Some remarks on tournament matrices
• Tournament matrices and their generalizations, I.
• On 4-Cycles and 5-Cycles in Regular Tournaments
• Hypertournament matrices, score vectors and eigenvalues
• On the characteristic roots of tournament matrices