Linear Systems of Differential Equations in Arrowhead Form

Abstract

This paper deals with different approaches for solving linear systems of the first order differential equations with the system matrix in the symmetric arrowhead form.Some needed algebraic properties of the symmetric arrowhead matrix are proposed.We investigate the form of invariant factors of the arrowhead matrix.Also the entries of the adjugate matrix of the characteristic matrix of the arrowhead matrix are considered. Some reductions techniques for linear systems of differential equations with the system matrix in the arrowhead form are presented.