### Teachings

Select Academic Year:     2017/2018 2018/2019 2019/2020 2020/2021 2021/2022 2022/2023
Professor
FEDERICA PES (Tit.)
Period
Second Semester
Teaching style
Convenzionale
Lingua Insegnamento
ITALIANO

Informazioni aggiuntive

Course Curriculum CFU Length(h)
[70/89]  ELECTRICAL, ELECTRONIC AND COMPUTER ENGINEERING [89/10 - Ord. 2016]  ELETTRICA 7 70
[70/89]  ELECTRICAL, ELECTRONIC AND COMPUTER ENGINEERING [89/20 - Ord. 2016]  ELETTRONICA 7 70
[70/89]  ELECTRICAL, ELECTRONIC AND COMPUTER ENGINEERING [89/30 - Ord. 2016]  INFORMATICA 7 70

### Objectives

Knowledge and Comprehension:
- Adequate knowledge and interpretation of the problems related to linear algebra and geometry;
- Ability to solve problems through the correct application of tools and methods of linear algebra and adequate geometric interpretation;
- Correct interpretation and use of the obtained results.

Judgment ability:
The student will be able to recognize the different problems of geometric nature appearing in different fields and to choose their correct and simpler solution.

Communication skills:
Correct use of the scientific language both in the oral and written form.

Ability of autonomous study:
The course solicits the students to study and work autonomously in order to be able to use various fonts in the scientific literature, different from the material provided by the teacher.

### Prerequisites

Basics on calculus, algebra, geometry, and trigonometry according to the usual outcomes of the secondary school.

### Contents

1 - Vectors in Euclidean space: operators on vectors, condition of linear independence, bases, orthonormal bases, scalar and vectorial product between vectors, mixed product. Complex numbers. (8 hours).

2 - Vector spaces, subspaces, dimension (7 hours)

3 - Matrices: operations between matrices, determinant of a matrix and their properties, Binet theorem, inverse matrix, matrix rank
(5 hours).

4 - Linear systems: reduction method, Rouché-Capelli theorem.
(14 hours).

5 - Recalls on functions, linear applications and matrices, and geometric examples; inverse of functions and matrices (8 hours)

6 - Eigenvalues and eigenvectors (9 hours).

7 - Abstract scalar products and complex case (9 hours)

8 - Advanced geometric applications: change of basis, orthogonal projections, reflections and rotations in the plane and in space, translations, conics and quadrics (10 hours)

### Teaching Methods

Lectures and exercises on the blackboard. In order to ensure greater effectiveness of the teaching activity, the lessons and exercises are seamlessly integrated with each other. At the same time as the course, there is also a tutoring activity aimed at assisting students in the study and preparation of the final exam. The teacher also provides constant assistance to students, throughout the academic year, both during office hours and through e-mail messages and teleconferencing systems.

### Verification of learning

The verification of learning takes place through a written test which lasts three hours and consists in carrying out some exercises, inherent to the entire program of the course, which require both operational skills and theoretical knowledge. A certain score is assigned to each exercise, which takes into account: correctness of the procedure followed, clarity of presentation, correctness of calculations.
The test is passed if the student has obtained a mark of not less than 18/30. The student has the right to request a subsequent oral test in order to improve the reported evaluation. Likewise, the teacher can request an oral test, if she deems it necessary in order to correctly evaluate the student's preparation.
To pass the exam, the student must demonstrate a basic knowledge of all the topics covered in the course. To achieve the maximum score, equal to 30/30, the student must demonstrate an excellent knowledge of the course topics.
For the A.Y. 2021-22 following the COVID-19 emergency, exams will be held face to face or remotely, subject to the indications provided by the University.

### Texts

Notes.

Consultation and in-depth book:
E. Schlesinger, Algebra Lineare e Geometria, Zanichelli