Ateneo - UPO

Vector spaces, bases, dimension. Eigenvalues and eigenvectors of square matrices and applications.

- Simon C.P -Blume L.E., Matematica 1 per l'Economia e le Scienze sociali, Università Bocconi Editore, 2002 (Cap. 15), presente in Biblioteca
- Simon C.P -Blume L.E., Matematica 2 per l'Economia e le Scienze sociali, Università Bocconi Editore, 2002 (Cap. 13), presente in Biblioteca

Knowledge and understanding of some basic notions of linear algebra and ability to use these notions in the analysis of some models.

It is recommended to take the exam of Mathematical Methods 2.

Lectures, tutorials.

Any useful information on the course and supplementary didactic resources can be found on the web page of the course at www.dir.uniupo.it.

A compulsory written exam consisting in:
- a question designed to test the level of knowledge achieved of the concepts considered;
- two exercises aimed to test the knowledge and understanding of the course contents, the ability to apply this knowledge and the ability to express the results obtained with a sufficiently rigorous technical language, with regard to the recognition of a vector space and the calculation of eigenvalues and eigenvectors of a square matrix.

There are 7 exam sessions in each solar year but students can enroll no more than three times, at their own choice. It is mandatory to register for the exam through the students portal: once the three exam participations have been reached, including withdrawals and refusals, the system will not allow further registrations.

Vector spaces and subspaces. Base and dimension of a vector subspace. Applications to linear algebraic systems.
Eigenvalues and eigenvectors of a real square matrix. Properties of eigenvalues, repeated eigenvalues and diagonalization of a square matrix. Eigenvalues and eigenvectors of symmetric, positive matrices. Applications: solution of scalar linear discrete dynamical systems, principal components of a random vector.

Achieving a good knowledge and understanding of the notions of vector space, eigenvalue and eigenvector.
Development of a good ability to recognize a vector space, determining a base, to calculate eigenvalues and eigenvectors in cases that can be manually treated.
Ability to apply the acquired knowledge to the study of some applied models.