66876 - Linear Algebra

Learning outcomes

At the end of the course, the student can handle the basic tools of linear algebra: he can solve linear sistems, he can operate within vector spaces (in particular he knows the concepts of linear independence, subspaces, basis and dimension) and with matrices (row-by-column product, inverse matrix), he is familiar with linear maps, eigenvectors and eigenvalues.

Course contents

Linear systems and the Gauss Algorithm for solving them. Vector spaces and subspaces of a vector space. Linear independent vectors and the vector space spanned by a set of vectors. Generators, basis and dimension of a vector space. Linear maps: definition and properties, kernel, image, the fundamental theorem. The matrix associated to a linar map. Isomorphisms between vector spaces. Structure theorem for the solutions of a linear system, Rouché-Capelli theorem. The determinant of a matrix, invertible matrix and computation of the inverse matrix. Change of bases in a vector space.When a linear map can be put in diagonal form.  Eigenvalues and eigenvectors of a linear map.

Teaching methods

Lessons in class and exercises

Assessment methods

The Linear Algebra course is paired with the Calculus course. The final grade is the average of the grades of the two courses.

After having passed the exam of one of the two courses, the student must pass the other exam in one year time, otherwise the first grade is not valid any more.
There is a written and a oral exam. It is compulsory to register for the written exam with AlmaEsami.
The written exam lasts 2 hours and consists on 4 exercises, containing also some small questions on the "theorical part". It is forbidden to use book, notes, calculators, notepads, etc. 
Only people who have a grade which is not less than 15/28 in the written exam are admitted to the oral exam. It is not necessary to register for the oral exam on AlmaEsami.

Links to further information

http://www.dm.unibo.it/~mmorigi/

Office hours

See the website of Marta Morigi