66876 - Linear Algebra

Learning outcomes

At the end of the module, the student understands and is able to use the basics of linear algebra: he is able to solve linear systems, solve problems in vector spaces and with the aid of vector spaces (in particular knows the concepts of linear independence, subspace, basis and dimension), multiply and invert matrices, study linear mappings (in particular knows the concepts of eigenvalue and eigenvector).

Course contents

• Linear systems and matrix algebra.
• Vector spaces; linear independence; bases and dimension. Subspaces associated to a matrix, rank.
• Linear maps and matrices. Linear systems.
• Determinant and inverse matrix.
• Change of basis; eigenvalues and eigenvectors.

Every week exercises will be given, that will be corrected by a tutor.

Readings/Bibliography

• Online lecture notes, weekly published during the course on the lecturer's personal web page.
• Introduzione all'algebra lineare, R. Fioresi, M. Morigi, edizioni CEA.

Teaching methods

Lectures.

Assessment methods

In order to pass the exam of the integrated course Mathematical Analysis - Linear Algebra on must pass the exam on each of the two parts; the grade of the integrated course is the mean of the grades of the two parts.

Linear Algebra exam: written and oral exams.

The written exam aims at verifying the ability of solving various problems, akin to those assigned during the course. It lasts 2 hours; it is forbidden to use books, notes or calculators; only paper and pen.

In order to attend the oral exam in a session one must achieve at least a grade 15/30 in a written exam of the same session.

The oral exam aims at verifying the knowledge of the theory developed during the course. Il lasts about half an our. 

Teaching tools

Lecture notes and exercises on the instructor's personal web page [http://www.dm.unibo.it/~regonati/rimini.html]

Office hours

See the website of Francesco Regonati