Jiyuan Tao

Some P-Properties for Nonlinear Transformations on Euclidean Jordan Algebras

In this article, we introduce the concepts of P and P0 properties for a nonlinear transformation defined on a Euclidean Jordan algebra and study existence of solution in the associated complementarity problems. In particular, we show, in this general setting, that if a transformation has the P0 and R0 properties, then all associated complementarity problems have solutions. We also describe a necessary condition for a transformation to have the (global) uniqueness of solution property.

Z-transformations on proper and symmetric cones: Z-transformations

Motivated by the similarities between the properties of Z-matrices on

The Cauchy interlacing theorem in simple Euclidean Jordan algebras and some consequences

R^{n}_+

A REPRESENTATION THEOREM FOR LYAPUNOV-LIKE TRANSFORMATIONS ON EUCLIDEAN JORDAN ALGEBRAS

and Lyapunov and Stein transformations on the semidefinite cone

A note on an inequality involving Jordan product in Euclidean Jordan algebras

\mathcal {S}^n_+

On the Uniform Nonsingularity Property for Linear Transformations on Euclidean Jordan Algebras

, 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.