


Politecnico di Torino  
Academic Year 2009/10  
01LQMDR, 01LQMAX, 01LQMJA 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 mathematic of hight school.

Syllabus
 Matrices (sum, products, rank, determinant, invertible matrix).
 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. A text of exercises with complete solutions can be find in my personal web page.

Bibliography
The english notes of the corse can be find in my personal web page.

Revisions / Exam
The examination consists in a written proof based on resolution of exercises and in an oral discussion about the main theorems proved during the course.
No calculator, no texts or notes can be used during the examination. 
