Extreme rays of certain cones of Hermitian forms
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- by Dragomir Ž. Djoković PDF
- Proc. Amer. Math. Soc. 83 (1981), 243-247 Request permission
Abstract:
Let $\mathcal {H}$ be the real vector space of hermitian forms on a finite-dimensional complex vector space $V$. For $f \in \mathcal {H}$ we denote by $\mathcal {H}(f)$ the closed convex cone in $\mathcal {H}$ consisting of forms $g$ such that $g(x,x) \geqslant 0$ for all $x$ satisfying $f(x,x) \geqslant 0$. Unless $f \leqslant 0$ and $f \ne 0$, the cone $\mathcal {H}(f)$ contains no nonzero subspaces of $\mathcal {H}$. Assuming that this is the case, we determine the extreme rays of $\mathcal {H}(f)$. The same problem is solved for real and quaternionic spaces.References
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Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 83 (1981), 243-247
- MSC: Primary 15A63; Secondary 46D05
- DOI: https://doi.org/10.1090/S0002-9939-1981-0624906-1
- MathSciNet review: 624906