# 65086 - Linear Algebra

### Course Unit Page

• Teacher Antonella Grassi

• Credits 10

• SSD MAT/03

• Language English

## 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

Vectorial and Euclidean structure of R^n; matrices; determinants; linear systems: exact solutions and least square solutions; linear applications; eingenvalues and eigenvectors; similarity of matrices and diagonalizable matrices; symmetric matrices and spectral decomposition; quadratic form; Jordan Form, singular value decomposition and pseudoinverse of a matrix and their applications.

Theory:

Lecture notes posted on e-learning platform

• "Introduction to Linear Algebra" Gilbert Strang, Wellesley Cambridge Press; video lectures are available here [http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/video-lectures/]

Exercises:

• material (exercise sheets, past written tests, etc) posted on the e-learning platform
• practice exams posted on the e-learning platform
• exercises from Strang’s and Treil’s books

## Teaching methods

Digital presentations and blackboards.

## Assessment methods

The exam consists of a mandatory written part and possibly followed by an oral part to be taken in the same exam session . (A detailed course syllabus will be published on the e-learning platform)

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 15/30.

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 total score will be the average of the written and oral part. 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 books, calculators or other electronic tools are allowed.

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

The calendar of the exams will be available on Almaesami.

To take both the written and the oral part, the student must show an identity document or the University badge.

## Office hours

See the website of Antonella Grassi