Spectral sets and functions on Euclidean Jordan algebras
| dc.contributor.advisor | Gowda, Muddappa S | |
| dc.contributor.author | Jeong, Juyoung | |
| dc.contributor.department | Mathematics and Statistics | |
| dc.contributor.program | Mathematics, Applied | |
| dc.date.accessioned | 2019-10-11T14:02:17Z | |
| dc.date.available | 2019-10-11T14:02:17Z | |
| dc.date.issued | 2017-01-01 | |
| dc.description.abstract | This thesis studies spectral and weakly spectral sets/functions on Euclidean Jordan algebras. These are generalizations of similar well-known concepts on the algebras of real symmetric and complex Hermitian matrices. A spectral set in a Euclidean Jordan algebra V is the inverse image of a permutation invariant set in R^n under the eigenvalue map (which takes an element x in V to its eigenvalue vector in R^n consisting of eigenvalues of x written in the decreasing order). A spectral function on V is the composition of a permutation invariant function on R^n and the eigenvalue map. In this thesis, we study properties of such sets/functions and show how they are related to algebra automorphisms and majorization. We show they are indeed invariant under algebra automorphisms of V, hence weakly spectral with converse holding when V is essentially simple. For a spectral set K, we discuss the transfer principle and a related metaformula. When K is also a cone, we show that the dual of K is a spectral cone under certain conditions. We also discuss the dimension of K, and characterize the pointedness/solidness of K. Specializing, we study permutation invariant (proper) polyhedral cones in R^n. We show that the Lyapunov rank of such a cone divides n. Lastly, we study Schur-convexity of a spectral function and describe some applications. | |
| dc.genre | dissertations | |
| dc.identifier | doi:10.13016/m2o7zj-ufbe | |
| dc.identifier.other | 11649 | |
| dc.identifier.uri | http://hdl.handle.net/11603/15685 | |
| dc.language | en | |
| dc.relation.isAvailableAt | The University of Maryland, Baltimore County (UMBC) | |
| dc.relation.ispartof | UMBC Mathematics and Statistics Department Collection | |
| dc.relation.ispartof | UMBC Theses and Dissertations Collection | |
| dc.relation.ispartof | UMBC Graduate School Collection | |
| dc.relation.ispartof | UMBC Student Collection | |
| dc.rights | This item may be protected under Title 17 of the U.S. Copyright Law. It is made available by UMBC for non-commercial research and education. For permission to publish or reproduce, please see http://aok.lib.umbc.edu/specoll/repro.php or contact Special Collections at speccoll(at)umbc.edu | |
| dc.source | Original File Name: Jeong_umbc_0434D_11649.pdf | |
| dc.subject | Algebra automorphism | |
| dc.subject | Euclidean Jordan algebra | |
| dc.subject | Majorization | |
| dc.subject | Optimization | |
| dc.subject | Spectral function | |
| dc.subject | Spectral set | |
| dc.title | Spectral sets and functions on Euclidean Jordan algebras | |
| dc.type | Text | |
| dcterms.accessRights | Distribution Rights granted to UMBC by the author. |