LINEAR ALGEBRA

The course is one of the basic activities of the Bachelor's Degree in Informatics. It aims at presenting 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, and geometric and computational applications. Ability to apply this knowledge in solving targeted exercises.

Elementary notions of mathematics of secondary school.

Fields and complex numbers. Linear equations and matrices, operations on matrices, special matrices. Real vector spaces: linear independence, bases and dimension, rank of a matrix.
Inner product, lines and planes. Linear transformations and matrices. Kernel and rank of a linear transformation. The matrix of a linear transformation. Vector space of matrices and linear transformations. Duality. Determinant, inverse matrix. Autovalues and autovectors. Diagonalisation.

Lecturer's slides and material (in italian).

Other book:
A. Facchini, Algebra e Matematica Discreta, Zanichelli 2000.

The exam consists of a written test (duration: two hours) composed of open-ended problems with the aim of verifying the students' ability to solve equations with complex numbers, parametric linear systems, analyze linear applications in abstract vector spaces and calculate eigenvalues ​​and eigenvectors of a matrix, showing that they know how to apply various calculation techniques, such as the determinant of a square matrix. The written test also includes a theoretical question aimed at assessing the level of understanding of the main notions introduced in the course. The test grade is given by the sum of the points assigned to the individual problems and the theoretical question. The exam can be passed with a minimum score of 18. The exam is open book.

Lectures delivered in presence.
A tutoring activity devoted to the resolution of exercises is planned.

written