


Politecnico di Torino  
Academic Year 2007/08  
05BCGHL, 05BCGHI Geometry 

1st degree and Bachelorlevel of the Bologna process in Computer Engineering  Verres/Ivrea 1st degree and Bachelorlevel of the Bologna process in Mechatronic Engineering  Verres/Ivrea 





Objectives of the course
Objectives of the course
The aim of the course is to introduce the theory of complex numbers, vector spaces, inear systems of equations, matrices and linear maps. Applications are then given to analytic geometry in the plane and in space. Prerequisites Elementary calculus. Elementary analytic geometry in the plane. 
Prerequisites
Elementary calculus. Elementary analytic geometry in the plane. 
Syllabus
Complex numbers. Polynomials. Vectors: sum, scalar product, wedge product. Vector spaces and subspaces. Bases and dimension. Scalar product in vector spaces. Orthonormal bases. Matrices; elementary operations and properties, rank. Linear Systems: the Gaussian elimination method, RouchéCapelli Theorem. Eigenvalues and eigenvectors. Diagonalization of matrices. Linear maps and associated matrices. Orthogonal matrices. Diagonalization of symmetric matrices. Quadratic forms and canonical forms. Analytic geometric in the plane and in the space. Conics. Quadrics. 
Bibliography
S. Greco, P. Valabrega, Lezioni di Geometria, volume 1, Levrotto e Bella N. Chiarli, S. Greco, P. Valabrega, 100 pagine di Geometria analitica dello spazio, Levrotto e Bella 
