On the Maximum of Entropy for Othogonal Matrices
The local and global bounds for the Shannon entropy of real orthogonal matrices have been found for various orders of orthogonal matrices. It has been proved that in the cases when a Hadamard matrix of order n exists, the entropy achieves its global maximum value n ln n. For other orders in which the corresponding Hadamard matrix does not exist, local maximal bounds on the entropy are obtained by making use of orthogonal matrices corresponding to nite projective planes, biplanes and triplanes. In the case of complex inverse orthogonal matrices, the construction has been shown, which achieves this global maximum bound. The Renyi and Tsallis entropy for real orthogonal matrices are also dened and their local and global optimal bounds are also obtained for various orders of n.
- Year: 2020
- Category: Secure & Resilient Systems
- Category: Radar Systems
- Tag: Shannon Entropy, Orthogonal Matrices, Optimization, Hadamard Matrices, Renyi Entropy, Tsallis Entropy, Kullback-Leibler Divergence
- Author: K. T. Arasu, Manil. T. Mohan, Akhilesh Pathak, Ramya Ramachandran Janaki
- Released: Indian Journal of Pure and Applied Mathematics
Featured Riverside Research Author(s)
K. T. Arasu
K. T. Arasu (Member, IEEE) is a senior research scientist at Riverside Research in the Engineering and Support Solutions Group. He received the B.S. and M.S. degrees in
mathematics from Panjab University, India, and the Ph.D. degree from The
Ohio State University. Prior to joining
Riverside Research, he was a Professor with the Department of Mathematics
and Statistics, Wright State University, for 35 years. He investigates novel
techniques on error correcting codes, cryptography, data security and privacy,
as well as topics at the intersection of machine learning, security, and
information theory. He has published over 110 research papers. During
his time as a professor at Wright State University, he was presented the
Teaching Excellence Award from the College of Science and Mathematics, the
Presidential Research Excellence Award, and the Trustees' Award for Faculty
Excellence. He serves on the editorial board of several technical international
journal publications.
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The above listed authors are current or former employees of Riverside Research. Authors affiliated with other institutions are listed on the full paper. It is the responsibility of the author to list material disclosures in each paper, where applicable – they are not listed here. This academic papers directory is published in accordance with federal guidance to make public and available academic research funded by the federal government.