65086 - LINEAR ALGEBRA

Conoscenze e abilità da conseguire

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

Contenuti

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.

Testi/Bibliografia

• "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.

 

Metodi didattici

The course consists of Theory, Applications and Exercises.

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

• Old Lecture notes
• Problem Sheets
• Solved Problems
• Old written exams
• Problems from Strang’s and Treil’s books

Recitation sessions with a Tutor

Office hours,  also online.

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

 

Modalità di verifica e valutazione dell'apprendimento

The exam consists of a mandatory written part, possibly followed by an oral part to be taken in the same exam session. Either the Instructor or the student may request the oral exam. The total score will be the average of the written and oral part. In order to take the oral exam the mark of the written part should be at least 16/30. When there is no request to take the oral exam the score of the written test will be the score for the course. The written and oral part cover the whole program.

The written part consists of a two hours exam of theory and proofs.  No calculators or others electronic tools are allowed.

The goal of the 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.

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.

Strumenti a supporto della didattica

Material posted on the e-learning platform Virtuale

Interactive Forum on Virtuale

 

In May or June there is a practice session onthe exam.

 

"L'insegnamento partecipa al progetto di innovazione didattica dell'Ateneo”.

Orario di ricevimento

Consulta il sito web di Antonella Grassi