R-Orbit Reflexive Operators
Functional Analysis
2011-12-09 v1
Abstract
We completely characterize orbit reflexivity and R-orbit reflexivity for square matrices over the real numbers. Unlike the complex case in which every matrix is orbit reflexive and C-orbit reflexivity is characterized solely in terms of the Jordan form, the orbit reflexivity and R-orbit reflexivity of a real matrix is described in terms of the linear dependence over Q of certain elements of R/Q. We also show that every n-by-n matrix over an uncountable field F is algebraically F-orbit reflexive.
Cite
@article{arxiv.1112.1904,
title = {R-Orbit Reflexive Operators},
author = {Don Hadwin and Ileana Ionascu and Hassan Yousefi},
journal= {arXiv preprint arXiv:1112.1904},
year = {2011}
}