# Regular and positive noncommutative rational functions

@article{Klep2017RegularAP,
title={Regular and positive noncommutative rational functions},
author={Igor Klep and James Eldred Pascoe and Jurij Vol{\vc}i{\vc}},
journal={J. Lond. Math. Soc.},
year={2017},
volume={95},
pages={613-632}
}
• Published 2017
• Mathematics, Computer Science
• J. Lond. Math. Soc.
Call a noncommutative rational function $r$ regular if it has no singularities, i.e., $r(X)$ is defined for all tuples of self-adjoint matrices $X$. In this article regular noncommutative rational functions $r$ are characterized via the properties of their (minimal size) linear systems realizations $r=c^* L^{-1}b$. It is shown that $r$ is regular if and only if $L=A_0+\sum_jA_j x_j$ is privileged. Roughly speaking, a linear pencil $L$ is privileged if, after a finite sequence of basis changes… Expand
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