Parametrization by polytopes of intersections of orbits by conjugation
| dc.creator | Leite, Ricardo S. | |
| dc.creator | Tomei, Carlos | |
| dc.date | 2001-07-06 | |
| dc.date.accessioned | 2026-07-07T04:42:30Z | |
| dc.date.available | 2026-07-07T04:42:30Z | |
| dc.description | Let S be an nXn real symmetric matrix with spectral decomposition S=Q^T Lambda Q, where Q is an orthogonal matrix and Lambda is diagonal with simple spectrum {lambda_1,..., lambda_n}. Also let O_S e R_S be the orbits by conjugation of S by, respectively, orthogonal matrices and upper triangular matrices with positive diagonal. Denote by F_S the intersection O_S and R_S. We show that the map F tha goes from the closure of F_S to R^n and takes S' = (Q')^T Lambda Q' to diag(Q' Lambda (Q')^T) is a smooth bijection onto its range P_S, the convex hull of some subset of the n! permuatations of (lambda_1, ..., lambda_n). We also find necessary and sufficient conditions for P_S to have n! vertices. | |
| dc.description | 21 pages, 2 figures, psfrag package | |
| dc.identifier | https://arxiv.org/abs/math/0107048 | |
| dc.identifier | http://arxiv.org/abs/math/0107048 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61811 | |
| dc.subject | Rings and Algebras | |
| dc.subject | 58F07 (Primary), 15A23 (Secondary) | |
| dc.title | Parametrization by polytopes of intersections of orbits by conjugation | |
| dc.type | text |