Quasi-commutativity of Entire Matrix Functions and the Continuous Analogue of the Resultant

Abstract

This paper is an addition to the paper [3], where it was proved that the theorem about the null space of the classical Sylvester resultant matrix also holds for its continuous analogue for entire matrix function provided that a certain so-called quasi-commutativity condition is fulfilled. In the present paper we show that this quasi-commutativity condition is not only sufficient but also necessary.

The third author gratefully acknowledges the support of the Glasberg-Klein Research Fund at the Technion.