Entropy and Hadamard matrices

doi:10.1088/0305-4470/36/7/103

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Entropy and Hadamard matrices

H Gopalkrishna Gadiyar et al 2003 J. Phys. A: Math. Gen. 36 L109-L112 doi: 10.1088/0305-4470/36/7/103

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H Gopalkrishna Gadiyar¹, K M Sangeeta Maini¹, R Padma¹ and H S Sharatchandra²
¹ AU-KBC Research Centre, M I T Campus, Anna University, Chromepet, Chennai 600 044, India
² Institute of Mathematical Sciences, C I T Campus, Taramani PO, Chennai 600 113, India
E-mail: gadiyar@au-kbc.org, sangeeta_maini@au-kbc.org, padma@au-kbc.org and sharat@imsc.res.in

Abstract. The entropy of an orthogonal matrix is defined. It provides a new interpretation of Hadamard matrices as those that saturate the bound for entropy. It appears to be a useful Morse function on the group manifold. It has sharp maximum and other saddle points. The matrices corresponding to the maxima for three and five dimensions are presented. They are integer matrices (up to a rescaling).

PACS numbers: 02.90.+p, 02.10.Eb

Mathematics Subject Classification: 05B20, 15A15, 94A17

Print publication: Issue 7 (21 February 2003)
Received 25 October 2002
Published 5 February 2003

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Entropy and Hadamard matrices

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