On Perron complements of totally nonnegative matrices (Q5935363)
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scientific article; zbMATH DE number 1610100
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On Perron complements of totally nonnegative matrices |
scientific article; zbMATH DE number 1610100 |
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On Perron complements of totally nonnegative matrices (English)
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26 June 2001
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The Perron complement of a principal submatrix of an irreducible totally nonnegative \(n\times n\) matrix \(A\) is discussed. Conditions are studied for which the Perron complement of a totally nonnegative matrix is also totally nonnegative. It is found that this complement is totally nonnegative if the complementary index set is based on consecutive indices. A quotient formula is derived for the Perron complement that is a reminiscent of the Haynsworth quotient formula for Schur complements.
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totally nonnegative matrices
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Perron complement
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irreducible
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Haynsworth quotient formula
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Schur complements
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