On semimonotone matrices with nonnegative principal minors (Q1873702)
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scientific article; zbMATH DE number 1917808
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On semimonotone matrices with nonnegative principal minors |
scientific article; zbMATH DE number 1917808 |
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On semimonotone matrices with nonnegative principal minors (English)
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27 May 2003
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The paper deals with two well-known classes of matrices in linear complementarity theory: semimonotone matrices (\(E_0\)-matrices) and matrices with all principal minors nonnegative (\(P_0\)-matrices). The author obtains two sets of conditions under which the two classes are identical. The first result asserts that if property (++) holds for a \(E_0\)-matrix, it must have nonnegative principal minors. The classes of hidden Minkowski matrices and Z-matrices satisfy property (++). The second set of conditions consists of a completely hidden Z-assumption on the matrix and an additional irreducibility requirement associated with each principal submatrix.
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\(P_0\)-matrix
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semimonotone matrix
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Z-matrix
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hidden Minkowski matrix
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linear complementarity problem
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nonnegative principal minors
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\(E_0\)-matrices
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0.9068058
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0.8950097
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0.89300394
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