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.

Attendance and participation in the training activities offered in the course and individual study will enable students to:

1. (Knowledge and understanding)
--- knowledge and understanding of the basic concepts on vector spaces, linear dependence and linearity;
--- knowledge and understanding of the basic concepts of Linear Algebra for the study of linear systems and applications and diagonalization of endomorphisms.

2.(Ability to apply knowledge and understanding)
-- ability to analyze the linear dependence of a set of vectors;
-- ability to study the linearity of a function and determine its kernel and image;
-- ability to analyze the existence and number of solutions of a parametric linear system, and possibly determine them;
-- ability to use matrix calculus, and in particular to determine the rank, kernel, image and determinant of a parametric matrix ;
-- ability to determine the diagonalizability of a parametric endomorphism, and to explicitly determine its eigenvalues and eigenvectors

3.(Judgment skills)
-- Ability to correctly interpret the statements of Linear Algebra.
-- Ability to apply the fundamental elements of Linear Algebra to address simple modeling problems.

Elementary notions of mathematics of secondary school.

Numeric fields and complex numbers. Introduction to the geometric vectors. Real vecotr spaces: linear independence and bases. Linear transformations: kernel and rank . Linear equations. Gauss elimination algorithm. Matrices: operations, special and invertible matrices..
Application of the matrices to the linear systems. Determinant of a square matrix. Autovalues and autovectors. Diagonalisation of a matrix. Inner product. Quadratic forms. Characterization of symmetric matrices.

Lecturer's slides and material.

Other book:
J. Liesen, V. Mehrmann, Linear Algebra, Springer 2015

he 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 exercises are designed to verify the abilities acquired during the course.

written

Assessment grid:

A. range 18-22
- sufficient knowledge and understanding of the program;

B. range 23-26
- fair knowledge and understanding of the program;
- fair rigor in conducting the exercises;

C. range 27-30
- good knowledge and understanding of the program,
- good rigor in conducting the exercises;

D. honors will be awarded in the presence of excellent knowledge and understanding of the program.

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