O estudo de determinantes sob a ótica do grupo de permutações

• Main Author: Moraes, Walter José Rodrigues de
• Publication Date: 2013
• Format: Master thesis
• Language: por
• Source: Repositório Institucional da UFG
• Download full: http://repositorio.bc.ufg.br/tede/handle/tde/2953
• topic: Grupos; Determinantes; Permutação; Determinants; Groups; Permutation; MATEMATICA::MATEMATICA APLICADA

The study of determinants development through the permutations made on their lines or columns dates back to 1812, a memory presented by Cauchy to the French Academy of Sciences. The present work is, in some way, a historical rescue. Firstly, a permutation is de ned: from a superior point of view there is a bijective application and, as such, the set of permutations has a group structure; from the elementary point of view, there is an ordainment of a group's elements. The fundamental fact is, secondly, that the de nition of determinant adjusts perfectly to both conceptions, based on the parity of the permutations. Based on the de nitions, the determinants properties are presented and, therefore, it is possible to proceed with the appropriate justi cations about their validity. A rule that associates each square matrix to a real number will de ne a real function of the variable matrix, the determinant function. This is the actual way in which determinants are presented in higher levels: the determinant is the unique alternated multilinear function of the lines (columns) of a square matrix, as indicated in [10]. By this presentation there is in mind the fact that it can be served as an inspiration to posterior studies.