Decomposição Matricial: uma incitação ao estudo de Álgebra Linear

Abstract

In this work, we carry out a study of the different methods of matrix decomposition, a fundamental theme in Linear Algebra as it provides computational ease and analytical simplicity. In practice it is unfeasible that most matrix calculations are done by: matrix inversion, linear system resolution and least squares method. Thus, decomposing matrices reveals their structures and characteristics, helping to interpret their meaning. The choice of methods to develop the work was the familiarity acquired during the courses of Linear Algebra and the need to do a scientific initiation within the Tutorial Education Program (PET). The objective was to study different methods of matrix decomposition, develop knowledge in content beyond those covered in graduation and present results through examples, whether studied or unpublished. First we study some basic concepts and later we introduce some fundamental matrix decomposition methods, such as: LU, LDU, Cholesky, Schur and QR. Therefore, this bibliographical research had as main references \cite{Hamilton}, \cite{Anton}, \cite{Vera}, \cite{Book}, \cite{Semat},\cite{Semap2020}, \cite {exampleSchur} and \cite{exampleSchur2}. The results achieved were the development of contents beyond what is seen in graduation, the presentation of studied and unpublished examples and the dissemination of an area that has attracted more and more researchers in Mathematics, Computer Science and Engineering. It is hoped that this work will serve as a basis for further research and contribute to the knowledge of the topic in initial training in Mathematics.