


Politecnico di Torino  
Academic Year 2007/08  
05BCGHK, 05BCGHG, 05BCGHJ, 05BCGHM, 05BCGJB Geometry 

1st degree and Bachelorlevel of the Bologna process in Computer Engineering  Torino 1st degree and Bachelorlevel of the Bologna process in Electronic Engineering  Torino 1st degree and Bachelorlevel of the Bologna process in Telecommunication Engineering  Torino Espandi... 





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.

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. 
Laboratories and/or exercises
These are supervised sessions in which students solve problems, either at the board or individually, under the supervision of a teacher.

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 
