Entropy and Hadamard Matrices
Mathematical Physics
2007-05-23 v2 math.MP
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 maxima and other saddle points. The matrices corresponding to the maxima for 3 and 5 dimensions are presented. They are integer matrices (upto a rescaling).
Cite
@article{arxiv.math-ph/0206018,
title = {Entropy and Hadamard Matrices},
author = {H. Gopalkrishna Gadiyar and K. M. Sangeeta Maini and R. Padma and H. S. Sharatchandra},
journal= {arXiv preprint arXiv:math-ph/0206018},
year = {2007}
}
Comments
7 pages, minor typographical errors corrected and conclusion added