LINEAR ALGEBRA

Basic course of the Bachelor's degree in Informatics.
The aim of the course is to present the fundamental ideas of linear algebra, gradually accustoming the student to the abstract concepts of mathematics.
A wide variety of geometric and practical applications will accompany the introduction of theoretical notions.

Knowledge and understanding of the fundamental linear algebra topics: linear systems, matrices, vector spaces, linear transformations, eigenvalues and eigenvectors, geometric and computational applications.
Ability to apply this knowledge in solving targeted exercises.

Elementary notions of mathematics of secondary school.

Fields and complex numbers.
Vectors of the plane and space: inner product and applications to the Euclidean geometry.
Linear systems and matrices: solutions of a linear system, elementary operations on the rows of a matrix, operations on matrices, special matrices.
Real vector spaces: linear dependence, bases and dimension of a vector space, vector supspaces.
Linear transformationsof vector spaces: kernel and rank, dimension theorem, matrix representation.
Dual vector space.
Determinant and rank of a matrix. Geometric interpretation of the determinant of a 3x3 matrix.
Eigenvalues and eigenvectors. Matrix diagonalisation. Spectral theorem.
Linear Algebra applications.

Lecturer's notes (in italian).

Other books:
M. Abate, C. de Fabritiis: Geometria analitica con elementi di algebra lineare, Seconda Edizione, McGraw-Hill, 2010.
A. Facchini, Algebra e Matematica Discreta, Zanichelli 2000.

The exam consists of a written test with theoretical and practical exercises aimed at verifying the acquisition of the required skills.

Lectures delivered online with the support of the e-learning tools.
Exercises will be carried out in class and assigned regularly at home.
The course includes a 45-hour specialized tutoring.

Italian

written