Tournament matrices and their generalizations, I.

Maybee, John S.; Pullman, Norman J.

doi:10.1080/03081089008818030

Cited by 28 publications

(28 citation statements)

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“…Then Moon and Pullman extended their idea to derive similar results for the generalized tournament matrices [21]. And, subsequently, Maybee and Pullman [18] considered more general matrices, the pseudo-tournament matrices, in which they introduced h-hypertournament matrices and showed that −1/2…”

Section: Introductionmentioning

confidence: 94%

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Some properties complementary to Brualdi-Li matrices

Wang

Yong

2015

Czech Math J

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Section: Introductionmentioning

confidence: 94%

“…The score vector can be used to obtain information about eigenvalues of A, see [16], [18]. Note that the score vector s satisfies s t · 1 = n(n − 1)/2 and s t s n(n − 1) 2 /4 with equality if and only if it is regular.…”

Section: Introductionmentioning

confidence: 99%

Some properties complementary to Brualdi-Li matrices

Wang

Yong

2015

Czech Math J

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“…( 1 . 1 ) This class of matrices was originally studied by Maybee & Pullman [13], and is a generalisation of the following classes of tournament-like matrices satisfying Eq. (1.1) that have received considerable attention in recent decades:…”

Section: Introductionmentioning

confidence: 99%

Pseudo-Tournament Matrices and Their Eigenvalues

Wang

Yong

2014

E Asian J Appl Math

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A tournament matrix and its corresponding directed graph both arise as a record of the outcomes of a round robin competition. An n × n complex matrix A is called h-pseudo-tournament if there exists a complex or real nonzero column vector h such that A + A* = hh* − I. This class of matrices is a generalisation of well-studied tournament-like matrices such as h-hypertournament matrices, generalised tournament matrices, tournament matrices, and elliptic matrices. We discuss the eigen-properties of an h-pseudo-tournament matrix, and obtain new results when the matrix specialises to one of these tournament-like matrices. Further, several results derived in previous articles prove to be corollaries of those reached here.

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“…The problem of pairwise comparison appears in various fields and scientists coming from very different areas have worked on this topic: mathematicians (Moon, 1968;Moon and Pullman, 1970;Monjardet, 1978;Reid and Beneke, 1978;Maybee and Pullman, 1990;Saary, 1994), statisticians (Kendall and Smith, 1940;David, 1963), social scientists (Fishburn, 1974(Fishburn, , 1977Moulin, 1983;Young, 1988), decision scientists (Roy and BOUYSSOU, 1992) and psychologists (Saaty, 1977). In this very extensive landscape we can make distinctions about both the nature of the data involved and the nature of the question raised.…”

Section: Introductionmentioning

confidence: 99%