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