A Path to Hadamard Matrices
There are characteristics of Hadamard matrices that enable an exhaustive search using algorithmic techniques. The search derives primarily from the eigenvalues which are constant after the Hadamard matrix is multiplied by its transpose. Generally this would be a performance concern but there are additional properties that enable the eigenvalues to be predicted. Here an algorithm is given to obtain a Hadamard matrix from a matrix of 1s using optimisation techniques on a row-by-row basis.
KeywordsHadamard Matrices eigen values optimization
Unable to display preview. Download preview PDF.
- 4.Klima, R.E., Sigmon, N.P., Stitzinger, E.L.: Applications of Abstract Algebra with MapleTM and Matlab®, 2nd edn. Chapman & Hall/CRC, Boca Raton (2006)Google Scholar
- 6.Orrick, W.P.: Switching operations for Hadamard matrices (2007), http://www.arxiv.org/abs/math.CO/0507515
- 8.Wallis, W.D., Street, A.P., Wallis, J.S.: Combinatorics: Room Squares, Sum-Free Sets, Hadmard Matrices. Springer, New York (1972)Google Scholar