Entropy and Hadamard Matrices
H. Gopalkrishna Gadiyar, K. M. Sangeeta Maini, R. Padma, H. S. Sharatchandra
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).
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