Gangster operators and invincibility of positive semidefinite matrices (Q603139)
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scientific article; zbMATH DE number 5811027
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Gangster operators and invincibility of positive semidefinite matrices |
scientific article; zbMATH DE number 5811027 |
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Gangster operators and invincibility of positive semidefinite matrices (English)
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5 November 2010
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It is not always true that after replacing in a positive semidefinite (\(psd\)) matrix \(A\) an opposite pair of entries by zero the matrix stays \(psd\). Call this operation of replacement a gangster operation (shooting holes in the matrix). In this paper properties of this operation are studied. This is one such problem: A \(psd\) matrix is called fully invincible if all gangster operations lead to \(psd\) matrices. This property is characterized. This has to do with M-matrices and comparison matrices.
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gangster operator
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invincible matrix
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positive semidefinite matrix
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M-matrices
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comparison matrices
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