skew Hadamard matrix

A Hadamard matrixMathworldPlanetmath H is skew Hadamard if H+HT=2I.

A collectionMathworldPlanetmath of skew Hadamard matrices, including at least one example of every order n100 and also including every equivalence classMathworldPlanetmathPlanetmath of order 28, is available this web page. It has been conjectured that one exists for every positive order divisible by 4.

Reid and Brown in 1972 showed that there exists a “doubly regularPlanetmathPlanetmath tournamentMathworldPlanetmath of order n” if and only if there exists a skew Hadamard matrix of order n+1.


  • 1 S. Georgiou, C. Koukouvinos, J. Seberry, Hadamard matrices, orthogonalMathworldPlanetmathPlanetmath designs and construction algorithms, pp. 133-205 in DESIGNS 2002: Further computational and constructive design theory, Kluwer 2003.
  • 2 K.B. Reid, E. Brown, Doubly regular tournaments are equivalentMathworldPlanetmathPlanetmathPlanetmath to skew Hadamard matrices, J. Combinatorial Theory A 12 (1972) 332-338.
  • 3 J. Seberry, M.Yamada, Hadamard matrices, sequences, and block designsMathworldPlanetmath, pp. 431-560 in Contemporary Design Theory, a collection of surveys (J.H.Dinitz & D.R.Stinson eds.), Wiley 1992.
Title skew Hadamard matrix
Canonical name SkewHadamardMatrix
Date of creation 2013-03-22 16:13:02
Last modified on 2013-03-22 16:13:02
Owner Mathprof (13753)
Last modified by Mathprof (13753)
Numerical id 13
Author Mathprof (13753)
Entry type Definition
Classification msc 15-00