Nonnegative matrices with doubly stochastic powers

dc.creatorBedford, Nancy Rosenblad
dc.description.abstractLet A be a nonnegative irreducible square matrix, and let m be an integer greater than one. Then it is possible to obtain the following necessary and sufficient conditions for A[raised m] to be doubly stochastic while A is not doubly stochastic. First, A is cyclic of index h, where h and m are not relatively prime. Also, there exist positive numbers [beta][lowered i] and [zeta][lowered i], i=l,...,h, such that the matrices A[lowered i] in a Frobenius normal form of A are respectively [beta][lowered i]/[beta][lowered i+1] stochastic, indices modulo h, and such that the matrices A[raised T, lowered i] are [zeta][lowered h-i]/[zeta][h-i+1] stochastic respectively, indices modulo h...
dc.description.departmentMathematics, Department of
dc.format.digitalOriginreformatted digital
dc.rightsThis item is protected by copyright but is made available here under a claim of fair use (17 U.S.C. Section 107) for non-profit research and educational purposes. Users of this work assume the responsibility for determining copyright status prior to reusing, publishing, or reproducing this item for purposes other than what is allowed by fair use or other copyright exemptions. Any reuse of this item in excess of fair use or other copyright exemptions requires express permission of the copyright holder.
dc.titleNonnegative matrices with doubly stochastic powers
dc.type.genreThesis, Department of of Houston of Science


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