Weisstein, Eric W.
The Wayback Machine - https://web.archive.org/web/20220103095234/https://mathworld.wolfram.com/TournamentMatrix.html
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A matrix for a round-robin tournament involving players competing in matches
(no ties allowed) having entries
This scoring system differs from that used to compute a score sequence of a tournament, in which a win gives one point and a loss zero points.
The matrix satisfies
where is the transpose
of (McCarthy and Benjamin 1996).
The tournament matrix for players has zero
determinant iff is odd
(McCarthy and Benjamin 1996). Furthermore, the dimension
of the null space of an -player tournament
matrix is
(McCarthy and Benjamin 1996).
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