Optimization of the Entropy Defined for an Orthogonal Matrix

Abstract

<p>The optimization bounds for the Shanon's entropy of an orthogonal matrix have been found for various classes of orthogonal matrices. It has been proved that in the cases when a Hadamard matrix exists, the entropy achieves it's maximum value. For other various cases in which Hadamard matrix does not exist, sharper bounds on the entropy has been found. A general proof for the optimization in case of other equivalent definitions of entropy has been produced.</p><p>This presentation occurred at the Wright State University Campus-Wide Celebration of Research, Scholarship and Creative Activities on April 8, 2011</p>