DESCRIPTION
This is an introduction to Analytical Geometry, that is, to the use of coordinates to study plane and spatia Euclidian Geometry. As they become necessary, the vectors are introduced, taking advantage of their great notational simplicity and their strong geometrical appeal.
Linear systems are shown as an example of the connection between Algebra and Geometry, motivating the consideration of matrices and linear dependence between their rows and columns. Areas and volumes lead to the study of determinants. Conics and quadrics lead to quadratic forms, to symmetric matrices and their eigenvalues.
In general, the book shows how basic concepts of Linear Algebra are useful for efficiently and elegantly handling Analytical Geometry problems.
ABOUT THE AUTHOR
Elon Lages Lima
He was Researcher Emeritus of the Instituto de Matemática Pura e Aplicada (IMPA) and a full member of the Brazilian Academy of Sciences and of the TWAS (Academy of Sciences for the Developing World). He was also Doctor Honoris Causa by the Federal Universities of Amazonas and of Alagoas and by the Universidad Nacional de Ingenieria del Perú, Professor Honoris Causa of the Federal Universities of Ceará and of Bahia, of the Universidade Estadual de Campinas, of the Pontificia Universidad Católica del Perú and the University of Brasília. Received the Order of Scientific Merit in the Class Grã-Cruz, from the Presidency of the Republic and the Award Anísio Teixeira, from the Ministry of Education and Culture.
He is the author of several books on Topology, Analysis, Algebra, and Elementary Mathematics, two of which received the Jabuti Award.
