## You are here

Homeskew Hadamard matrix

## Primary tabs

# skew Hadamard matrix

A Hadamard matrix $H$ is *skew Hadamard* if $H+H^{T}=2I$.

A collection of skew Hadamard matrices, including at least one example of every order $n\leq 100$ and also including every equivalence class of order $\leq 28$, is available at 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 regular tournament of order n” if and only if there exists a skew Hadamard matrix of order n+1.

# References

- 1
S. Georgiou, C. Koukouvinos, J. Seberry,
*Hadamard matrices, orthogonal 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 equivalent to skew Hadamard matrices*, J. Combinatorial Theory A 12 (1972) 332-338. - 3
J. Seberry, M.Yamada,
*Hadamard matrices, sequences, and block designs*, pp. 431-560 in Contemporary Design Theory, a collection of surveys (J.H.Dinitz & D.R.Stinson eds.), Wiley 1992.

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

15-00*no label found*

- Forums
- Planetary Bugs
- HS/Secondary
- University/Tertiary
- Graduate/Advanced
- Industry/Practice
- Research Topics
- LaTeX help
- Math Comptetitions
- Math History
- Math Humor
- PlanetMath Comments
- PlanetMath System Updates and News
- PlanetMath help
- PlanetMath.ORG
- Strategic Communications Development
- The Math Pub
- Testing messages (ignore)

- Other useful stuff
- Corrections