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Abstract

Let B be an n x n doubly substochastic matrix and let s be the sum of all entries of B. In this paper we show that B has a sub-defect of k which can be computed by taking the ceiling of (n-s) if and only if there exists an (n+k) x (n+k) doubly stochastic extension containing B as a submatrix and k minimal. We also propose a procedure constructing a minimal completion of B, and then express it as a convex combination of partial permutation matrices.

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File nameDate UploadedVisibilityFile size
A_Minimal_Completion_of_Doubly_Stochastic_Matrix.tex
18 Jul 2022
Public
49.4 kB
0-Fall2015_TIM_talk.pdf
18 Jul 2022
Public
464 kB

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Metadata

  • Subject
    • Mathematics

  • Institution
    • Gainesville

  • Event location
    • Nesbitt 3218

  • Event date
    • 25 March 2016

  • Date submitted

    18 July 2022

  • Additional information
    • Acknowledgements:

      Dr. Selcuk Koyuncu