Irreducible matrices with reducible principal submatrices (Q1300911)
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scientific article; zbMATH DE number 1331378
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Irreducible matrices with reducible principal submatrices |
scientific article; zbMATH DE number 1331378 |
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Irreducible matrices with reducible principal submatrices (English)
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9 February 2000
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Let \(A\) denote a \((0, 1)\)-matrix of order \(n\geq 3\). The author shows that if \(A\) is irreducible and all of its principal submatrices of order \(n-1\) are reducible, then the total number of off-diagonal 0's in the \(i\)th row and the \(i\)th column of \(A\) is at least \(n-1\) for \(i= 1,\dots, n\).
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irreducible matrix
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strongly connected digraph
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primal subgraph
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principal submatrices
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0.8216784596443176
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0.7702142000198364
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0.7499861717224121
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