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Algebra

Code: 103795
Credits: 6
2026/2027
Degree programme Type Course
Electronic Engineering for Telecommunications FB 1
Telecommunication Systems Engineering FB 1

Contact lecturer

Name :
Gil Solanes Farres
Email :
gil.solanes@uab.cat

Teaching staff

Pol Orobitg Bernades

Group languages

You can consult this information at the end of the document.

Prerequisites

There are no prerequisites. However, it would be beneficial for the student to have a solid understanding of the concepts of rational numbers, real numbers, and complex numbers. It is also advisable that they be familiar with some method for solving systems of linear equations.

Objectives

This is an introduction to the most basic aspects of Linear Algebra, with an emphasis on the functional and instrumental aspects of linear techniques, without forgetting the necessary conceptual basis.

The most important underlying goal is to learn how to design efficient strategies for applying specific techniques to solve complex problems.

Learning outcomes

Electronic Engineering for Telecommunications
  • KU100 (Identify elementary mathematical models and tools of calculus, linear algebra and differential equations in telecommunications engineering.) Identify elementary mathematical models and tools of calculus, linear algebra and differential equations in telecommunications engineering.
  • KU101 (Interpret random phenomena using probability theory and statistics.) Interpret random phenomena using probability theory and statistics.
  • KU102 (Associate the main methods of matrix decomposition with their practical applications in telecommunications engineering.) Associate the main methods of matrix decomposition with their practical applications in telecommunications engineering.
  • SU111 (Express themselves appropriately using basic mathematical language in telecommunications engineering.) Express themselves appropriately using basic mathematical language in telecommunications engineering.
Telecommunication Systems Engineering
  • KU100 (Identify elementary mathematical models and tools of calculus, linear algebra and differential equations in telecommunications engineering.) Identify elementary mathematical models and tools of calculus, linear algebra and differential equations in telecommunications engineering.
  • KU101 (Interpret random phenomena using probability theory and statistics.) Interpret random phenomena using probability theory and statistics.
  • KU102 (Associate the main methods of matrix decomposition with their practical applications in telecommunications engineering.) Associate the main methods of matrix decomposition with their practical applications in telecommunications engineering.
  • SU111 (Express themselves appropriately using basic mathematical language in telecommunications engineering.) Express themselves appropriately using basic mathematical language in telecommunications engineering.

Contents

1. Matrices

Matrices. Operations with matrices. Special matrices: symmetric, Toeplitz, circulant, invertible, Hermitian, orthogonal.

Elementary row transformations. Gauss–Jordan normal form of a matrix. Rank of a matrix.

Invertibility criterion and computation of inverse matrices.

Systems of linear equations and linear varieties. Gaussian elimination method. Direction vectors and dimension of linear varieties. Rouché’s theorem.


2. Vector Spaces

Definition of a vector space and examples. Linear combinations of vectors. Subspaces. Generating sets.

Linear dependence of vectors. Criterion for linear dependence.

Bases, dimension, and coordinates. Working with coordinates. Change of basis.

Linear mappings. Matrix associated with a linear map. Composition of linear maps. Kernel and image subspaces of a linear map. Isomorphisms.


3. Diagonalization of matrices

Eigenvalues and eigenvectors of a square matrix. Diagonalization criterion.

Applications of diagonalization: computing powers of matrices and solving systems of linear differential equations with constant coefficients.

Learning activities and methodology

Title Hours ECTS Learning outcomes
Personal study of the theory 36 1.44
Individual problem solving 61.5 2.46
Lectures 36 1.44
Problem sessions 12 0.48

The central part of the learning process is the student’s own work. The role of the instructor is to support the student in this task by providing information or pointing out sources where it can be found, and guiding their progress so that the learning process can be carried out effectively. In line with these ideas, and according to the course objectives, the development of the course will be based on the following activities:

  • Lecture classes. The scientific and technical knowledge related to the subject will be presented in the form of lectures. These classes will introduce the basic concepts outlined in the syllabus and provide clear guidance on how to complete and deepen this content.
  • Problem-solving classes. These sessions will build on the scientific and technical knowledge introduced in the lectures, with the aim of reinforcing and deepening understanding. Basic techniques will be practiced through the resolution of practical exercises.

Note: 15 minutes of one class, scheduled in accordance with the center’s or degree program’s calendar, will be set aside for students to complete surveys evaluating the instructor’s performance and the course/module.

Annotation: within the schedule set by the centre or degree programme, 15 minutes of one class will be reserved for students to evaluate their lecturers and their courses or modules through questionnaires.

Assessment

Continuous assessment activities

Title Weight Hours ECTS Learning outcomes
Mid-term exam 0.35 2 0.08 KU100, SU111
Follow-up tests 0.15 0.5 0.02 KU100, KU101, KU102, SU111
Final exam 0.5 2 0.08 KU100, KU101, KU102, SU111

Assessment will be continuous and individual. It will consist of the following:

  • A mid-term exam during the first part of the semester, worth 35% of the final grade.
  • A final exam at the end of the semester, worth 50% of the final grade.
  • In-class follow-up tests, globally worth 15% of the final grade.

The final course grade is the weighted average of the midterm and final exams and the follow-up tests, provided that the average of the midterm and final exams is at least 3.5 out of 10. If this condition is not met, the final grade will not exceed 3.5 out of 10.

If the final grade is 5 or higher, the course is considered passed and cannot be reassessed.

If the final grade is below 5, the student may opt for a reassessment, as described below, provided that they have completed activities representing at least 60% of the total course grade.

Reassessment consists of a comprehensive exam covering the entire course. If the grade obtained in this exam is 3.5 or higher, a weighted average will be calculated using 85% from the exam and 15% from the follow-up tests.

If this average is 5 or higher, the final grade will be a pass with a 5. Otherwise, the course will be failed with the obtained grade.

Students who opt for the single assessment system will take two exams equivalent to the midterms and one test equivalent to the follow-up tests in a single day. The weights, reassessment and other aspects of the assessment will be the same as for continuous assessment.

The awarding of an Honors Distinction (Matrícula d'Honor) is at the discretion of the course instructors. UAB regulations state that Honors Distinctions may only be granted to students with a final grade of 9 or higher, and may be awarded to up to 5% of enrolled students.

A student will be considered Not Assessable (NA) if they do not complete at least 50% of thecourse’s assessment activities.

For the midterm exams, the instructor will set a date for students to submit claims or questions about the grade received.


At the professors’ discretion, in cases where it is deemed appropriate, any written test must subsequently be validated with an oral test. In the event of discrepancies between the results of the two assessments, the oral test will prevail.


Without prejudice to other disciplinary measures that may be deemed appropriate, and in accordance with current academic regulations, any irregularity committed by a student that could affect the outcome of an assessment will be penalized with a grade of zero. This means that cheating or allowing others to cheat on any activity will result in a zero for that activity, and if that activity is required to pass, the entire course will be failed.

Assessment activities graded in this manner cannot be retaken, and the course will therefore be failed with no option for recovery during the academic year.

There will be no differentiated treatment for students who repeat the subject.


Bibliography

1. M. Masdeu, A. Ruiz, Apunts d'Àlgebra Lineal,
https://mat.uab.cat/~albert/wp/wp-content/uploads/2020/02/MR_Apunts_d__lgebra_Lineal2020.pdf
2. E. Nart X. Xarles, Apunts d'àlgebra lineal, Materials de la UAB, núm. 237, 1a edició.
3. S. I. Grossman, Álgebra lineal con aplicaciones, McGraw-Hill, 1991.
5. P. Lancaster, Theory of Matrices, Academic Press, NY, 1969.
6. J. Arvesu, F.J. Marcellán, J. Sánchex Ruiz, Problemas resueltos de álgebra lineal , S.A. EDICIONES PARANINFO

Software

No specific software will be used.

Course groups and languages

The information provided is provisional until November 30. After this date, you will be able to consult the language of each group through this link. To access the information, you will need to enter the course CODE

Type of teaching Group Language Semester Shift
(TE) Theory 31 Catalan first semester morning-mixed
(TE) Theory 33 Catalan first semester morning-mixed
(PAUL) Classroom practices 311 Catalan/Spanish first semester morning-mixed
(PAUL) Classroom practices 312 Catalan/Spanish first semester morning-mixed
(PAUL) Classroom practices 331 Catalan/Spanish first semester morning-mixed
(PAUL) Classroom practices 332 Catalan/Spanish first semester morning-mixed