O teorema da representação de riesz.

Abstract

In this work, we will present one of the most relevant results when studying linear functionalities in Linear Algebra or Functional Analysis, the famous Riez Represen-tation Theorem, where we will perform an algebraic analysis. In this, we prove that every linear functional can be represented by an internal product dened in a Vector Space. A linear functional is nothing more than a linear application of any vector space in a scalar body. We will restrict our study to only nite-dimensional vector spaces and to the scalar body the set of real numbers R. This result for spaces of innite dimension is seen in Functional Analysis, the discipline of a postgraduate in mathematics. our goal. Thus, the work was based on bibliographical research, searching for academic papers and books that deal with this subject. With this, we make les of these works, where we dismember concepts, theorems, demonstrations that were of paramount importance for the understanding of the theme.