The semigroup of real stochastic matrices and generalized inversion

dc.contributor.advisorDecell, Henry P., Jr.
dc.contributor.advisorSinkhorn, Richard D.
dc.contributor.committeeMemberLloyd, Tom
dc.contributor.committeeMemberFriedberg, Michael
dc.contributor.committeeMemberShieh, Leang-San
dc.creatorLan, Shaw-Ping
dc.description.abstractThe theory of generalized inversion plays an important role in numerical analysis, least-squares theory, statistical estimation, network analysis, and many other areas of pure and applied mathematics. In this dissertation properties of the generalized inverse of a real stochastic matrix (nonnegativity removed) are developed, and applications are made to the locally compact affine semigroup of the real stochastic matrices. Necessary and sufficient conditions under which the generalized inverse of a real stochastic matrix is real stochastic are established. Additional results concerning the Brazen inverse, Brazen ordering and group inverse of the real stochastic matrices are included. The set Tn consisting of In (the nxn identity) and all elements of the real stochastic semigroup which do not belong to the core of any idempotent is characterized as those matrices of the form B [equals] In 4 [plus] A, where Ae [equals] 6 and AA[plus]e [equals] e. Other related results and unsolved problems are stated.
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.subjectMatrix inversion
dc.titleThe semigroup of real stochastic matrices and generalized inversion
dc.type.genreThesis of Natural Sciences and Mathematics, Department of of Houston of Philosophy


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