00005 - Algebra

Course Unit Page

Academic Year 2019/2020

Learning outcomes

The aim of this course is to provide a standard introduction to linear algebra and matrix analysis.
Students should:
- be familiar with basic concepts and properties of finite dimensional real vector spaces
- be familiar with algebra of real matrices
- be able to solve linear systems
- be familiar with basic concepts and properties of euclidean spaces
- have acquaintance of linear transformation between vector spaces and their representation by matrices
- be able to diagonalize a linear operator or a square matrix
- be able to classify real quadratic forms.

Course contents

Finite dimensional real vector spaces. Subspaces, linear dependence, bases and dimension.
Matrix algebra. Rank of a matrix. Determinants. Systems of linear equations.
Linear transformations and matrices. Change of basis. Diagonalization of a matrix.
Inner product spaces: norms , distances, orthogonal vectors. Orthogonal projections and least squares solutions for a linear system. Diagonalization of symmetric matrices, spectral theorem.
Real quadratic forms. Positive definite (semi)definite quadratic forms.


Lecture notes downloadable from the lecturer site.
L. Robbiano, Linear Algebra for everyone, Springer Verlag 2010
C.D. Meyer, Matrix Analysis and Applied Linear Algebra, SIAM, 2000.

Teaching methods

Lessons ex cathedra. Classroom exercises, homework

Assessment methods

Written examination, where is possible to use calculators and self made formularies. The detailed explanation of all the passages is strongly requested. The aim of the exam is to detect the capability of the student to face both theoretical and practical problems in Linear Algebra.

Teaching tools

Lessons ex-cathedra using video beamer and blackboard. Homework. Computer algebra exercises.

The teaching material presented in class will be made available to the student in electronic format through the university's institutional portal. Username and password are reserved for students enrolled at the University of Bologna.


The teacher responds to e-mail messages, duly signed by the student with Name, Surname and matriculation number, and which concern appointment requests or topics that are not covered by the course information presented here.


Links to further information


Office hours

See the website of Daniele Ritelli