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.
Matrices: definitions, operation on matrices, special matrices. Determinant and rank of a matrix.
Real vector spaces: definitions, bases and dimension of a vector space, vector subspaces, scalar product of R^n, orthogonal and orthonormal bases and matrices.
Linear transformations: definitions, associated matrices, image and kernel.
Linear systems: solutions of a linear system, interpretation with respect to linear transformations, Gauss elimination method.
Affine spaces: definitions, euclidean plane and space.
Eigenvalues and eigenvectors: change of bases, matrix diagonalisation. Spectral theorem.
Linear Algebra applications.

Lecturer's slides and material (in italian).

Other book:
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 in presence and streamed.
A tutoring activity devoted to the resolution of exercises is planned.

Italian

written