Transformações lineares no plano e aplicações
Carregando...
Data
2013-03-15
Autores
Título da Revista
ISSN da Revista
Título de Volume
Editor
Universidade Federal de Goiás
Resumo
This paper begins with a brief history about the development of vector spaces and linear
transformations, then presents fundamental concepts for the study of Linear Algebra, with
greater focus on linear operators in the R2 space. Through examples it explores a wide
range of operators in R2 in order to show other applications of matrices in high school
and prepares the ground for the presentation a version of Spectral Theorem for selfadjoint
operators in R2, which says that for every operator self-adjoint T : E!E in finite
dimensional vector space with inner product, exists an orthonormal basis fu1; : : : ;ung E
formed by eigenvectors of T, and culminates with their applications on the study of conic
sections, quadratic forms and equations of second degree in x and y; on the study of
operators associated to quadratic forms, a version of Spectral Theorem could be called
as The Main Axis Theorem albeit this nomenclature is not used in this paper. Thereby
summarizing a study made by Lagrange in "Recherche d’arithmétique ", between 1773
and 1775, which he studied the property of numbers that are the sum of two squares.
Thus he was led to study the effects of linear transformation with integer coefficients in a
quadratic form in two variables.
Descrição
Palavras-chave
Citação
NOGUEIRA, Leonardo Bernardes. Transformações lineares no plano e aplicações. 2013. 62 f. Dissertação (Mestrado Profissional em Matemática em Rede Nacional) - Universidade Federal de Goiás, Goiânia, 2013.