Spectral sets and functions on Euclidean Jordan algebras
نویسندگان
چکیده
منابع مشابه
Löwner's Operator and Spectral Functions in Euclidean Jordan Algebras
We study analyticity, differentiability, and semismoothness of Löwner’s operator and spectral functions under the framework of Euclidean Jordan algebras. In particular, we show that many optimization-related classical results in the symmetric matrix space can be generalized within this framework. For example, the metric projection operator over any symmetric cone defined in a Euclidean Jordan a...
متن کاملSpectral functions on Jordan algebras: differentiability and convexity properties
A spectral function on a formally real Jordan algebra is a real-valued function which depends only on the eigenvalues of its argument. One convenient way to create them is to start from a function f : R 7→ R which is symmetric in the components of its argument, and to define the function F (u) := f(λ(u)) where λ(u) is the vector of eigenvalues of u. In this paper, we show that this construction...
متن کاملSparse Recovery on Euclidean Jordan Algebras
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 ...
متن کاملThe Fischer-Burmeister Complementarity Function on Euclidean Jordan Algebras∗
∗The work was partly supported by a Discovery Grant from NSERC, and the National Natural Science Foundation of China (10671010, 70640420143). 1 Lingchen Kong, Department of Combinatorics and Optimization, Faculty of Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada; Department of Applied Mathematics, Beijing Jiaotong University, Beijing 100044, P. R. China (e-mail: konglche...
متن کاملMore results on Schur complements in Euclidean Jordan algebras
In a recent article [8], Gowda and Sznajder studied the concept of Schur complement in Euclidean Jordan algebras and described Schur determinantal and Haynsworth inertia formulas. In this article, we establish some more results on the Schur complement. Specifically, we prove, in the setting of Euclidean Jordan algebras, an analogue of the Crabtree-Haynsworth quotient formula and show that any S...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2017
ISSN: 0024-3795
DOI: 10.1016/j.laa.2016.12.020