O estudo de determinantes sob a ótica do grupo de permutações
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2013-02-28
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Universidade Federal de Goiás
Resumo
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.
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Moraes, Walter José Rodrigues de - O estudo de determinantes sob a ótica do grupo de permutações - 2013 - 45 f. - Dissertação - Programa de Pós-graduação em Matemática (IME) - Universidade Federal de Goiás - Goiânia - Goiás - Brasil.