65086 - Linear Algebra

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 to solve linear systems - be familiar with basic concepts and properties of euclidean spaces - master linear transformations 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

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; singular value decomposition and pseudoinverse of a matrix and their application to the least square solution problem.

 

A detailed course program will be available at the end of the course on AMS Campus.

Readings/Bibliography

Theory:

• lecture notes posted on AMS campus
• "Linear Algebra and its applications" David C. Lay Addison-Wesley
• "Linear Algebra" Jim Hefferon  (for the first part of the program)
• "Introduction to Linear Algebra" Gilbert Strang, Wellesley Cambridge Press; video lectures are available here

Exercises:

• material (exercise sheets, past written tests,...) posted on AMS campus
• "Exercises and problems in linear algebra" J. M. Erdman
• "Exercise and solution manual for a First Course in Linear Algebra" R. A. Beezer

Teaching methods

Blackboard and/or digital presentation.

Assessment methods

The exam consists of a written part and an oral one both compulsory and on the whole program (see course contents published at the end of the course on AMS Campus [https://campus.unibo.it/]] ).

The written part has the aim to test the ability of using linear tools to solve exercises and problems and lasts two hours. During the written test the students are allowed (and advised) to use books, lecture notes, calculator,...

There will be an optional midterm test (at the end of the third mini-semester) on the first part of the course contents.

In order to take the oral exam the score of the written part should be at least 15/30.

The oral exam has the aim to test the theoretical knowledge and the comprehension of the topic developed during the course and the ability of using correctly the mathematical formalism. It starts with a discussion about the written test. Then the student should answer in writing to at least two open questions.

The calendar of the exams is available on Almaesami  and it is compulsory to register on Almaesami  only for the written test. To take both the written and the oral part, the student must show an identity document or the Universitary badge.

 

Teaching tools

Lecture notes on the topics developed during the lessons will be available on AMS campus, as well as exercises and previous years written tests.

 

The tutor of the course is Dott. Alessandro Mella.

Office hours

See the website of Alessia Cattabriga