Vinnikov, Victor (Ben Gurion Univ.)

Singularities of Noncommutative Rational Functions and Minimal Realizations

Scheduled for presentation during the Mini-Symposium "Polynomial Inequalities and Applications II" (TuA07), Tuesday, July 25, 2006, 10:50−11:15, Room H

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on May 27, 2023

Abstract

We show that the singularities of a matrix valued noncommutative rational function coincide with the singularities of the resolvent of a linear pencil in its minimal realization. This is essential, among other things, for some powerful applications of noncommutative realization techniques to problems in noncommutative convexity and noncommutative real semialgebraic geometry. The proof is based on a certain noncommutative differential calculus.