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<p>For a given <i>I</i> × <i>J</i> doubly substochastic matrix <i>A</i>, by adding a (cardinal) number of columns or rows, we want to obtain a doubly stochastic matrix <i>D</i> that contains <i>A</i> as a sub-matrix. Then it is shown that there are minimal (cardinal) numbers of such cardinal numbers, which we call row sub-defect and column sub-defect of <i>A</i>. We also try to obtain these two values in some cases.</p>

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Minimal completion of I × J doubly substochastic matrices

  • 期刊论文

  • 发表日期：

    2025年2月26日

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  • Mohammad Dadkhah,
  • Ali Bayati Eshkaftaki,
  • Seyed Mahmoud Manjegani

摘要

For a given I × J doubly substochastic matrix A, by adding a (cardinal) number of columns or rows, we want to obtain a doubly stochastic matrix D that contains A as a sub-matrix. Then it is shown that there are minimal (cardinal) numbers of such cardinal numbers, which we call row sub-defect and column sub-defect of A. We also try to obtain these two values in some cases.