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