Doubly Stochastic Processing on Jacket Matrices

Jia HOU  Moon Ho LEE  Kwangjae LEE  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E89-A   No.11   pp.3368-3372
Publication Date: 2006/11/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e89-a.11.3368
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: General Fundamentals and Boundaries
doubly stochastic processing,  Hadamard matrices,  unitary decomposition,  orthostochastic,  

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In this letter, we define the generalized doubly stochastic processing via Jacket matrices of order-2n and 2n with the integer, n≥2. Different from the Hadamard factorization scheme, we propose a more general case to obtain a set of doubly stochastic matrices according to decomposition of the fundaments of Jacket matrices. From order-2n and order-2n Jacket matrices, we always have the orthostochastoc case, which is the same as that of the Hadamard matrices, if the eigenvalue λ1 = 1, the other ones are zeros. In the case of doubly stochastic, the eigenvalues should lead to nonnegative elements in the probability matrix. The results can be applied to stochastic signal processing, pattern analysis and orthogonal designs.