On the pencil of a matrix and its applications

Abstract

The present thesis is an important contribution of matrix theory and its applications. It consists of an introduction and (04) chapters. In the first one, we review certain basic definitions about pencils where we introduce the concept of invariant polynomials. The second and the third chapters are dedicated to the application of of pencils in order to solve implicit differential systems by two approaches of the mathematicians: F.R. Gantmacher, S.L Campbell. In the last chapter, we apply the pencil of matrices zA+B to find a solution to any discrete degenerate systems also, we provide an example to illustrate the given method then, we ended our thesis by general conclusion and a bibliography listing 22 titles.