1. Z-transformations on proper and symmetric cones.
- Author
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Gowda, M. and Tao, Jiyuan
- Subjects
- *
MATRICES (Mathematics) , *LYAPUNOV functions , *CONES (Operator theory) , *MATHEMATICAL transformations , *QUADRATIC fields , *LORENTZ transformations - Abstract
Motivated by the similarities between the properties of Z-matrices on $$R^{n}_+$$ and Lyapunov and Stein transformations on the semidefinite cone $$\mathcal {S}^n_+$$ , we introduce and study Z-transformations on proper cones. We show that many properties of Z-matrices extend to Z-transformations. We describe the diagonal stability of such a transformation on a symmetric cone by means of quadratic representations. Finally, we study the equivalence of Q and P properties of Z-transformations on symmetric cones. In particular, we prove such an equivalence on the Lorentz cone. [ABSTRACT FROM AUTHOR]
- Published
- 2009
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