Perron vector ordering for a subclass of tournament matrices
type: Item
instance of: scholarly article
title: Perron vector ordering for a subclass of tournament matrices
zbMATH Open document ID: 0935.15007
DOI: 10.1016/S0024-3795(98)10249-5
published in: Linear Algebra and its Applications
publication date: 2000-04-25T00:00:00Z
review text: This paper gives formulas for the Perron vector of a tournament matrix having score vector \([1, 1, 2, 3,\dots, n-3,n-2, n-2]^t\). This offers some insight into the relation between the ranking of tournament results by the score vector, and the Kendall-Wei proposal of ranking by the size order of the Perron-vector entries [cf. \textit{M. G. Kendall}, Biometrics 11, 43-62 (1955) and \textit{T. H. Wei}, The algebraic foundations of ranking theory, Ph.D. Thesis, Cambridge Univ., Cambridge (1952)]. In particular, a characterization is offered of all matrices of this type for which the two rankings are equivalent.
reviewed by: David Steinsaltz
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 15B57
zbMATH DE Number: 1331322
zbMATH Keywords: Perron vectors
zbMATH Keywords: tournament matrices
zbMATH Keywords: score vectors
zbMATH Keywords: Kendall-Wei method
author: S. J. Kirkland
MaRDI profile type: Publication
cites work: Q4326384
cites work: Q3346350
cites work: Q3867835
cites work: Algebraic multiplicity of the eigenvalues of a tournament matrix
cites work: On the minimum Perron value for an irreducible tournament matrix
cites work: A note on Perron vectors for almost regular tournament matrices
cites work: Q5585195
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description: scientific article; zbMATH DE number 1331322