Publications de l'Institut Mathématique, Nouvelle Série Vol. 93(107), pp. 117–126 (2013) 

TOTAL REDUCTION OF LINEAR SYSTEMS OF OPERATOR EQUATIONS WITH THE SYSTEM MATRIX IN THE COMPANION FORMIvana JovovicFaculty of Electrical Engineering, University of Belgrade, Belgrade, SerbiaAbstract: We consider a total reduction of a nonhomogeneous linear system of operator equations with the system matrix in the companion form. Totally reduced system obtained in this manner is completely decoupled, i.e., it is a system with separated variables. We introduce a method for the total reduction, not by a change of basis, but by finding the adjugate matrix of the characteristic matrix of the system matrix. We also indicate how this technique may be used to connect differential transcendence of the solution with the coefficients of the system. Keywords: Partial and total reduction for linear systems of operator equations, characteristic polynomial, characteristic matrix, adjugate matrix, rational and Jordan canonical forms, invariant factors, differentially algebraic function, differentially transcendental function. Classification (MSC2000): 15A21 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 2 Apr 2013. This page was last modified: 8 Apr 2013.
© 2013 Mathematical Institute of the Serbian Academy of Science and Arts
