The doubly graded matrix cone and Ferrers matrices (Q1399239)
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scientific article; zbMATH DE number 1956799
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The doubly graded matrix cone and Ferrers matrices |
scientific article; zbMATH DE number 1956799 |
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The doubly graded matrix cone and Ferrers matrices (English)
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30 July 2003
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A doubly graded (\(n\times m\)) matrix, by definition, is a nonnegative matrix with each row and column nonincreasing. The polyhedral cone \(\mathcal M\) consisting of all doubly graded matrices is studied: the faces are determined and related to the Ferrers matrices; different subsets of \(\mathcal M\) are investigated. The problem of the existence of an integral doubly graded matrix with given line sums is studied as well.
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nonnegative matrix
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doubly graded matrix
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doubly graded matrix cone
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doubly substochastic matrix
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Ferrers matrix
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majorization
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partition
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polyhedral cone
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