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Abstract:
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The optimization bounds for the Shannon's entropy of an orthogonal matrix have been found for the various classes of orthogonal matrices. A universal upper bound on the entropy for all n
has been analytically proved and that it is achievable if and only if Hadamard matrix for that n exists. For the cases of n≡1,2,3 (mod 4) sharper bounds have been found. For n=3,5,6,10 we have analytically proved the result using Householder reflections given by Stewart. For the general n two results have been obtained for the problem through Lie groups. |
