Jordan quadratic SSM-property and its relation to copositive linear transformations on Euclidean Jordan algebras
نویسندگان
چکیده
منابع مشابه
On the Uniform Nonsingularity Property for Linear Transformations on Euclidean Jordan Algebras
In a recent paper, Chua and Yi introduced the so-called uniform nonsingularity property for a nonlinear transformation on a Euclidean Jordan algebra and showed that it implies the global uniqueness property in the context of symmetric cone complementarity problems. In a related paper, Chua, Lin, and Yi raise the question of converse. In this paper, we show that, for linear transformations, the ...
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The P, Z, and S properties of a linear transformation on a Euclidean Jordan algebra are generalizations of the corresponding properties of a square matrix on R. Motivated by the equivalence of P and S properties for a Z-matrix [2] and a similar result for Lyapunov and Stein transformations on the space of real symmetric matrices [6], [5], in this paper, we present two results supporting the con...
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A real square matrix is said to be a P-matrix if all its principal minors are positive. It is well known that this property is equivalent to: the nonsign-reversal property based on the componentwise product of vectors, the order P-property based on the minimum and maximum of vectors, uniqueness property in the standard linear complementarity problem, (Lipschitzian) homeomorphism property of the...
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Generalizing the P-property of a matrix, Gowda et al. [Gowda, M. S., R. Sznajder, J. Tao. 2004. Some P-properties for linear transformations on Euclidean Jordan algebras. Linear Algebra Appl. 393 203–232] recently introduced and studied Pand globally uniquely solvable (GUS)-properties for linear transformations defined on Euclidean Jordan algebras. In this paper, we study the invariance of thes...
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Let L be a linear transformation on a finite dimensional real Hilbert space H and K be a closed convex cone with dual K in H . The cone spectrum of L relative to K is the set of all real λ for which the linear complementarity problem x ∈ K, y = L(x)− λx ∈ K, and 〈x, y〉 = 0 admits a nonzero solution x. In the setting of a Euclidean Jordan algebra H and the corresponding symmetric cone K, we disc...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2010
ISSN: 0024-3795
DOI: 10.1016/j.laa.2010.03.005