Czechoslovak Mathematical Journal

Czechoslovak Mathematical Journal, first online, pp. 1-12

Minimal completion of $I\times J$ doubly substochastic matrices

Mohammad Dadkhah, Ali Bayati Eshkaftaki, Seyed Mahmoud Manjegani

Received October 30, 2024. Published online February 26, 2025.

Abstract: For a given $I\times J$ 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.

Keywords: doubly (sub)stochastic; minimal completion; semi-infinite; row sub-defect; column sub-defect

Classification MSC: 15A03, 15A83, 15A04, 47L05

DOI: 10.21136/CMJ.2025.0450-24

PDF available at: Springer Institute of Mathematics CAS

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Affiliations: Mohammad Dadkhah, Ali Bayati Eshkaftaki (corresponding author), Department of Mathematics, Faculty of Mathematical Sciences, Shahrekord University, P.O. Box 115, Shahrekord 88186-34141, Iran, e-mail: mdmathiran@yahoo.com, bayati.ali@sku.ac.ir; Seyed Mahmoud Manjegani, Department of Mathematical Sciences, Isfahan University of Technology, Iran, Department of Mathematics and Statistics, University of Regina, 3737 Wasacana Parkway, Regina Saskatchewan, S4S 0A2, Canada, e-mail: manjgani@cc.iut.ac.ir, manjeg1s@uregina.ca

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