نتایج جستجو برای: ‎euclidean jordan algebra‎

تعداد نتایج: 106254  

2015
Baha Alzalg

In this paper, we study and analyze the algebraic structure of the circular cone. We establish a new efficient spectral decomposition, set up the Jordan algebra associated with the circular cone, and prove that this algebra forms a Euclidean Jordan algebra with a certain inner product. We then show that the cone of squares of this Euclidean Jordan algebra is indeed the circular cone itself. The...

2014
Vasco Moço Mano

Considering the Euclidean Jordan algebra of the real symmetric matrices endowed with the Jordan product and the inner product given by the usual trace of matrices, we construct an alternating Schur series with an element of the Jordan frame associated to the adjacency matrix of a strongly regular graph. From this series we establish necessary conditions for the existence of strongly regular gra...

Journal: :Math. Oper. Res. 2006
M. Seetharama Gowda Roman Sznajder

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...

2013
Lingchen Kong Jie Sun Jiyuan Tao Naihua Xiu

We consider the sparse recovery problem on Euclidean Jordan algebra (SREJA), which includes sparse signal recovery and low-rank symmetric matrix recovery as special cases. We introduce the restricted isometry property, null space property (NSP), and s-goodness for linear transformations in s-sparse element recovery on Euclidean Jordan algebra (SREJA), all of which provide sufficient conditions ...

2011
Vasco Moço Mano António de Almeida Vieira

We consider a strongly regular graph, G, with adjacency matrix A, and associate a three dimensional Euclidean Jordan algebra to A. Then, by considering convergent series of Hadamard powers of the idempotents of the unique complete system of orthogonal idempotents of the Euclidean Jordan algebra associated to A, we establish new admissibility conditions for the existence of strongly regular grap...

Journal: :communication in combinatorics and optimization 0
behrouz kheirfam azarbaijan shahid madani university

in this paper, we present a full newton step feasible interior-pointmethod for circular cone optimization by using euclidean jordanalgebra. the search direction is based on the nesterov-todd scalingscheme, and only full-newton step is used at each iteration.furthermore, we derive the iteration bound that coincides with thecurrently best known iteration bound for small-update methods.

Journal: :European Journal of Operational Research 2006
Domingos Moreira Cardoso Luís Almeida Vieira

The properties of the barrier F (x) = −log(det(x)), defined over the cone of squares of a Euclidean Jordan algebra, are analyzed using pure algebraic techniques. Furthermore, relating the Carathéodory number of a symmetric cone with the rank of an underlying Euclidean Jordan algebra, conclusions about the optimal parameter of F are suitably obtained. Namely, in a more direct and suitable way th...

2016
M. Seetharama Gowda

A positive map between Euclidean Jordan algebras is a (symmetric cone) order preserving linear map. We show that the norm of such a map is attained at the unit element, thus obtaining an analog of the operator/matrix theoretic Russo-Dye theorem. A doubly stochastic map between Euclidean Jordan algebras is a positive, unital, and trace preserving map. We relate such maps to Jordan algebra automo...

2011
M. Seetharama Gowda Jiyuan Tao

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...

2013
Bo Kyung Choi Gue Myung Lee

*Correspondence: [email protected] Department of Applied Mathematics, Pukyong National University, Busan, 608-737, Korea Abstract A linear optimization problem over a symmetric cone, defined in a Euclidean Jordan algebra and called a self-scaled optimization problem (SOP), is considered. We formulate an algorithm for a large-update primal-dual interior-point method (IPM) for the SOP by using a p...

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