65086 - Linear Algebra

Course Unit Page


This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda.

Quality education Gender equality

Academic Year 2021/2022

Learning outcomes

The aim of this course is to provide a standard introduction to linear algebra and matrix analysis. By the end of the course the student should: - be familiar with basic concepts and properties of finite dimensional real vector spaces - be familiar with algebra of real matrices - be able solve linear systems - be familiar with basic concepts and properties of euclidean spaces - understand the meaning of least square solution of a linear system and be able to find it - master linear transformations between vector spaces and their representation by matrices - be able to diagonalize, if possible, a linear operator or a square matrix and to find the spectral decomposition of a symmetric operator or matrix

Course contents

Linear systems. Matrices. Linear systems and matrices. Properties of matrices, operation on matrices. Solutions of homogeneous and non-homegenous linear systems. Vector spaces, especially finite dimensional vector spaces. Linear transformations. Linear transformation and matrices. The determinant; properties and applications. Inner product spaces. Projections. Exact solutions and least square solutions of linear systems. Eingenvalues and eigenvectors; similarity of matrices and diagonalizable matrices. Symmetric matrices and spectral decomposition. Quadratic forms and matrices. Jordan Form, Singular value decomposition. Applications.

The detailed syllabus is published on Virtuale.


"Introduction to Linear Algebra" Gilbert Strang, Wellesley Cambridge Press

  • "Linear Algebra Done Wrong" S. Treil

A. Grassi: Lecture notes posted on e-learning platform Virtuale.


Teaching methods

The course consists of Theory, Applications and Exercises.

Material posted on the e-learning platform Virtuale, including:

  • Problem Sheets,
  • Solved Problems
  • Past written exams
  • Problems from Strang’s and Treil’s books

Recitation sessions with a Tutor

Online Office Hours on the Online plattform Forum

Assigned problems, to be solved individually and in group and/or during the Recitation Sessions with the Tutor.

Assessment methods

The exam consists of a mandatory written part, followed by an oral part to be taken in the same exam session.

The written exam is an open book open notes 90 minute exam. No calculators or other electronic tools are allowed.

In order to take the oral exam the mark of the written part should be at least 16/30. The grade of the course is a combination of the written and oral exam.

The written and oral exam cover the whole program. The goal of both written and oral exam is to verify the understanding of the material covered in the course and the ability to solve problems.

The oral exam will start with a discussion of the written test.

The calendar of the exams is posted on Almaesami.

While the exams will be held online, the sign up period for the written exam ends a week before the exam.

Before starting the written and the oral part, a student must show The University ID.


Teaching tools

Material posted on the e-learning platform Virtuale


In May or June there is a Practice Session on how to take the written online exam. It will be possible to sign up for the Practice Session  on AlmaEsami.

Office hours

See the website of Antonella Grassi