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Families of complex Hadamard matrices
Stockholm University, Faculty of Science, Department of Physics.
2013 (English)In: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 438, no 7, 2929-2957 p.Article in journal (Refereed) Published
Abstract [en]

What is the dimension of a smooth family of complex Hadamard matrices including the Fourier matrix? We address this problem with a power series expansion. Studying all dimensions up to 100 we find that the first order result is misleading unless the dimension is 6, or a power of a prime. In general the answer depends critically on the prime number decomposition of the dimension. Our results suggest that a general theory is possible. We discuss the case of dimension 12 in detail, and argue that the solution consists of two 13-dimensional families intersecting in a previously known 9-dimensional family. A precise conjecture for all dimensions equal to a prime times another prime squared is formulated.

Place, publisher, year, edition, pages
2013. Vol. 438, no 7, 2929-2957 p.
Keyword [en]
Hadamard matrices
National Category
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-88997DOI: 10.1016/j.laa.2012.10.029ISI: 000315830200006OAI: oai:DiVA.org:su-88997DiVA: diva2:615281
Note

AuthorCount:2;

Available from: 2013-04-09 Created: 2013-04-08 Last updated: 2017-12-06Bibliographically approved

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Bengtsson, Ingemar
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