A characterization of convex cones of matrices with constant regular inertia (Q1590643)
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scientific article; zbMATH DE number 1547885
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A characterization of convex cones of matrices with constant regular inertia |
scientific article; zbMATH DE number 1547885 |
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A characterization of convex cones of matrices with constant regular inertia (English)
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19 July 2001
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A necessary and sufficient condition is found for a convex cone of complex \(n\times n\) matrices to contain matrices with constant regular inertia. This condition is of the form \(\text{Re} (x^*HAx)>0\) for every non-zero vector \(x\) and a Hermitian matrix. The procedure uses the extreme point method and is based on a version of the Lyapunov equation. The work is an extension of a previous paper of the authors [ibid. 250, 105-131 (1997; Zbl 0871.15012)].
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convex cone
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regular inertia
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Hermitian matrix
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extreme point method
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Lyapunov equation
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