\(F\)-matrices (Q2735557)
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scientific article; zbMATH DE number 1640523
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(F\)-matrices |
scientific article; zbMATH DE number 1640523 |
Statements
15 June 2002
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Hadamard inequality
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Fischer inequality
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totally nonnegative matrices
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\(F\)-matrices
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inverse \(F\)-matrices
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\(W\)-matrices
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\(F\)-matrices (English)
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\(F\)-matrices are matrices such that each principal minor is nonnegative and also each principal minor satisfies Fischer's inequality. The authors characterize the case of equality in Hadamard's inequality, show the inverse as well as the original have positive minors, give a condition for the inverse of an \(F\)-matrix to be an \(F\)-matrix, and show matrices satisfying the hypothesis of the Drazin-Haynsworth theorem (\(W\)-matrices) are \(F\)-matrices, as well as their inverses.
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