


Politecnico di Torino  
Academic Year 2009/10  
01AAWDR, 01AAWAX, 01AAWJA Linear Algebra 

1st degree and Bachelorlevel of the Bologna process in Mechanical Engineering  Vercelli 1st degree and Bachelorlevel of the Bologna process in Civil Engineering  Vercelli 1st degree and Bachelorlevel of the Bologna process in Electronic And Computer Engineering  Vercelli 





Objectives of the course
The goal of this course is to learn the fundamental tools of linear algebra which are basic for engineering applications.

Expected skills
At the end of the course the student will be able to use matrix calculus, to solve linear systems,
to compute dimension, bases, intersections and unions of vector and subvector spaces, to compute eigenvalues, eigenvectors with applications to diagonalization of square matrices and to the study of conics in the plane. 
Prerequisites
The students are expected to know results and techniques from trigonometry, complex numbers and basic mathematics of high school.

Syllabus
 Matrices (sum, products, rank, determinant, invertible matrices).
 Linear systems (Gauss algorithm , RouchèCapelli's Theorem, Cramer's Theorem).  Vector spaces (geometrical meaning, basis, dimension, subspaces: intersection sum and direct sum).  Linear applications (Kernel, images, composition).  Eigenvalues and eigenvectors , similarity to diagonal matrices.  Euclidean spaces (norm for vectors, orthonormal basis). Spectral Theorem and quadratic forms.  Geometry in coordinates of the plane (line and conics). 
Laboratories and/or exercises
Exercise sections are done during the course.

Bibliography
M. Ferrarotti, Appunti di Algebra lineare , Ed. Otto.
Saranno disponibili in rete dispense del docente. M.L. Spreafico, Esercizi relativi al corso di Algebra lineare , disponibili presso Politeko. Testi di consultazione e di esercizi: N. Chiarli, S. Greco, P. Valabrega, 100 esercizi di... Algebra Lineare, ed. Levrotto e Bella. N. Chiarli, S. Greco, P. Valabrega, 100 esercizi di... Geometria analitica piana, ed. Levrotto e Bella. S.Greco, P.Valabrega, Lezioni di Geometria, ed. Levrotto e Bella. A.Sanini, Elementi di Geometria, Levrotto e Bella. 
Revisions / Exam
The examination consists in a written proof based on resolution of exercises and in an oral discussion about the subjects contained in the program.
No calculator, no texts or notes can be used during the examination. 
