ABSTRACT
The theory of integral equations, especially of linear integral equations, may be considered as an extension of linear algebra as well as precursory of functional analysis. The analogies between Algebra and Analysis and the idea to consider the functional equations, i.e. equations where the unknown is a function, as borderline cases of algebraic equations goes back to the beginning of infinitesimal calculus, which, in a certain way, fulfills a need of generalization from finite to infinite. This chapter first proposes a nuclear form of a matrix, and then, presents the Fredholm's determinant. Subsequently, Fredholm’s alternative is also presented. If the function g is limited and S-continuous on T and if det (I + Ak) is not infinitesimal, the Fredholm’s equation (I+AK)f=g has a unique solution f which is S-continuous and limited.
