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Proceedings of the American Mathematical Society

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Extreme rays of certain cones of Hermitian forms

Author: Dragomir Ž. Djoković
Journal: Proc. Amer. Math. Soc. 83 (1981), 243-247
MSC: Primary 15A63; Secondary 46D05
MathSciNet review: 624906
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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.

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Keywords: Hermitian form, positive definite, signature, radical, real quaternions, convex cone, extreme ray
Article copyright: © Copyright 1981 American Mathematical Society

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