Positive linear functionals and the order cone (Q1124650)
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scientific article; zbMATH DE number 4112782
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Positive linear functionals and the order cone |
scientific article; zbMATH DE number 4112782 |
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Positive linear functionals and the order cone (English)
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1989
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Let P be the cone of \(n\times n\) complex matrices with positive semi- definite Hermitean part and let \(P^*\) be the dual cone. The paper shows equality of two expressions defined for \(p\in \partial P\) and q arbitrary, namely max Re(cq) over all \(c\in P^*\) satisfying \(cI=1\) and \(Re(cp)=0\) equals max Re(\(\xi\),q\(\xi)\) over all vectors \(\xi\) of norm one satisfying \((p+p^*)\xi =0\).
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cone of complex matrices
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positive linear functionals
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order cone
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dual cone
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