ECTS credits ECTS credits: 6
ECTS Hours Rules/Memories Student's work ECTS: 97 Hours of tutorials: 3 Expository Class: 25 Interactive Classroom: 25 Total: 150
Use languages Spanish, Galician
Type: Ordinary Degree Subject RD 1393/2007 - 822/2021
Departments: Mathematics
Areas: Algebra
Center Higher Technical Engineering School
Call: First Semester
Teaching: With teaching
Enrolment: Enrollable | 1st year (Yes)
A general aim, shared with other subjects of mathematics, is to became familiar with the language and the mathematical methods, improving the capacity of reasoning, analysis, synthesis and formulation of arguments.
Other specific aims of the subject are:
- To know and to handle the concepts and the techniques of the Linear Algebra and the Euclidean Geometry that are detailed in the program.
- To apply techniques of matrix algebra.
- To solve systems of linear equations.
- Geometric interpretation of some results.
1.- (Lectures: 6 hours, seminar: 2 hours and laboratory: 4 hours).
- Matrix algebra:
Matrix. Operations with matrices. Elementary matrix. Echelon form. Rank of a matrix. Determinant of a square matrix. Properties and calculation of determinants. Inverse of a matrix.
2.-(Lectures: 3 hours, seminar: 1 hour and laboratory: 2 hours).
- Systems of linear equations:
Matrix form of a system of linear equations. Equivalent systems. Solving systems of linear equations: Gauss method and Cramer's rule.
3.-(Lectures: 6 hours, seminar: 2 hours and laboratory: 3 hours)..
- Vector spaces:
Vectorial spaces and subspaces. Linear independence. Basis and dimension.
4.-(Lectures: 5 hours, seminar: 2 hours and laboratory: 3 hours).
- Linear maps:
Linear transformations. Kernel and image. Matrix of a linear transformation. Matrix of change of basis. Rank of a linear transformation. Relation to the solution of a system of linear equations.
5.-(Lectures: 3 hours, seminar: 2 hours and laboratory: 2 hours).
- Diagonalization:
Eigenvalues and eigenvectors. Polynomial rings K [x]. Characteristic polynomial. Matrix diagonalization and similarity.
6.-(Lectures: 2 hours, seminar: 1 hour and laboratory: 1 hour).
- Scalar product and orthogonality:
Scalar product. Distances. Orthogonality. Orthogonal projection.
Basic:
-MERINO, L.; SANTOS, E., Álgebra Lineal con métodos elementales, Thomson, 2006.
-RIVERO, Ó., Álxebra Lineal e Multilineal, Edicións USC, 2025.
Complementary:
-ARVESÚ, J.; MARCELLÁN, F.; SÁNCHEZ, J., Problemas resueltos de Álgebra Lineal, Thomson, 2005.
-BURGOS, J., Álgebra finita y lineal. García-Maroto Editores, 2010.
-HERNÁNDEZ, E. "Álgebra Lineal y Geometría". Addison-Wesley/Universidad Autónoma de Madrid, 1994.
-LARSON, R.; EDWARDS, B.; FOLVO, D.C., Álgebra Lineal, Pirámide, 2004.
To help to reach the general competences and transversals as stated in the Memory of the Title of Degree in Computer Engineering of the USC (CG8, CG9, CG10, TR1, TR2, TR3 and FB1).
The module/thematic group competences that are worked in this course are:
- To explain and argue in a clear way the hypotheses and developments used in problem solving, using appropriate terminology.
- To develop the ability to analyze and solve problems.
- Organizing and planning ability.
- To master mathematical notation, method and terminology for modeling and case study.
- To improve the communicating ability, both spoken and written.
In addition this subject will allow to reach the following specific competences:
- To know the basic concepts of Linear Algebra: linear dependence and independence, basis, changes of basis, operations and equations of subspaces, linear transformations, etc.
- To know the algorithms to reduce matrix to echelon forms and to be able to apply them to the calculation of the rank, calculation of bases, system resolution, etc.
- To understand the intimate relation among matrices, linear transformations and systems of linear equations.
- To be able to analyze if a matrix is diagonalizable and, in its case, to diagonalize it.
- To know some examples of Euclidean spaces and to handle in the real n-dimensional space the scalar product , Gram-Schmidt's method and the orthogonal projection to solve some geometric problems.
The general methodological indications established in the Memory of Title of Degree in Computer Engineering of the USC will be followed.
The lectures, in big groups, will consist basically of the presentation by the teacher of the theoretical concepts, some examples and the showing of results that are more useful to the comprehension of the subject (working on competences CG8, CG10 and TR3).
The seminar interactive classes that will serve to illustrate the theoretical contents, will consist in the resolution of questions and exercises by the teacher with the participation of students (working on competences CG9 and TR3).
In the laboratory interactive classes, there will be a major implication of the student, giving priority to a more active and personalized pedagogy, and they will be devoted to solving problems, under the supervision of the teacher, which will also contribute to the acquisition of practical skills and to the illustration of the theoretical contents (working on competences CG9, CG10, TR1,TR2 and FB1).
Assigment proposals will be done (either individual and / or in group) throughout the four-month period (working on competences CG9, CG10, TR1 and TR2).
In the tutorials in very limited groups, a personalized follow-up of student learning and out-of-class work will be carried out (working on competences CG8, TR1 and TR2).
We will open a course in the Virtual Campus in which, in addition to having various support materials, we will keep a daily record of what is treated in each class meeting, as well as exercices for work in laboratory interactive classes.
Teaching will be face-to-face. Tutorials and communication with students can be face-to-face or virtual. In the virtual case they can be asynchronous, through the virtual course forums or e-mail, or synchronous, through the MS Teams platform.
There is a call with two opportunities.
The students’ grade, including repeaters, will be based on the evaluation of a final theoretical-practical exam (F) and on the continuous assessment of the work carried out throughout the semester (C).
For continuous assessment (C), both the test that will be done halfway through the semester and the assignments requested by the professors will be taken into account, as well as the student's participation in classes and tutorials. The grade obtained (C) is valid for both opportunities of the course.
All enrolled students may sit, on the dates indicated in the School’s exam calendar, for the theoretical-practical test that will be held in January and, if the subject is not passed, for the one that will be held in June.
The final grade, in each of the opportunities, will be calculated using the formula:
Final grade = 70%F + 30%C
A student will be considered “Not presented” if they do not attend either of the two final exams.
To pass the subject, the student must obtain at least a 4.5 in the final exam (F). If a student gets at least a 5 in the final exam (F), they will pass the subject.
In cases of fraudulent completion of exercises or exams, the provisions of the Regulations on the evaluation of academic performance of students and grade review will apply.
Regarding point 1 of the USC’s regulations on class attendance in official undergraduate and master's studies, it is indicated that class attendance will not be assessed.
The final theoretical-practical exam will be in-person and written.
ON-SITE WORK AT CLASSROOM:
- Lectures: 25 hours
- Learning based on problems in limited groups: 10 hours
- Practical meetings in limited groups: 15 hours
- Tutorials in very small groups: 3 hours
- Activities of assessment: 5 hours.
- Total on-site work: 58 hours
STUDENT PERSONAL WORK (NON ON-SITE): 92 hours
TOTAL: 150 hours (6 credits ECTS)
Continuous attendance to classes.
So as the classes are useful it is necessary to study the subject explained day by day.
It is essential that students come to classes in limited groups ,previously working the exercises proposed for every session. For this it is necessary to have enough knowledge on the theory that allows to approach the above mentioned problems.
The bibliography books are to complement the classes, in them it could be found both the results explained at class and an important source of examples and exercises.
Xabier Garcia Martinez
- Department
- Mathematics
- Area
- Algebra
- xabier.garcia [at] usc.es
- Category
- Professor: University Lecturer
Oscar Rivero Salgado
- Department
- Mathematics
- Area
- Algebra
- oscar.rivero [at] usc.es
- Category
- Professor: LOU (Organic Law for Universities) PhD Assistant Professor
Ana Peon Nieto
- Department
- Mathematics
- Area
- Algebra
- ana.peon [at] usc.es
- Category
- PROFESOR/A PERMANENTE LABORAL
| Monday | |||
|---|---|---|---|
| 11:00-12:00 | Grupo /CLE_01 | Galician, Spanish | Classroom A1 |
| 18:00-19:30 | Grupo /CLIL_04 | - | Computer Room I7 |
| Tuesday | |||
| 11:00-12:00 | Grupo /CLE_01 | Galician, Spanish | Classroom A1 |
| 18:00-19:30 | Grupo /CLIL_05 | Spanish, Galician | Computer Room I7 |
| Wednesday | |||
| 10:00-11:00 | Grupo /CLIS_01 | Spanish | PROJECTS |
| 11:00-12:00 | Grupo /CLIS_02 | Spanish | Classroom A1 |
| 18:00-19:30 | Grupo /CLIL_01 | Galician | Computer Room I7 |
| Thursday | |||
| 11:00-12:00 | Grupo /CLIS_03 | Spanish, Galician | Classroom A1 |
| 18:00-19:30 | Grupo /CLIL_02 | Galician, Spanish | Computer Room I7 |
| Friday | |||
| 18:00-19:30 | Grupo /CLIL_03 | Galician | Computer Room I7 |
| 01.12.2026 10:00-14:00 | Grupo /CLIS_01 | Classroom A1 |
| 01.12.2026 10:00-14:00 | Grupo /CLIS_02 | Classroom A1 |
| 01.12.2026 10:00-14:00 | Grupo /CLIL_01 | Classroom A1 |
| 01.12.2026 10:00-14:00 | Grupo /CLIL_02 | Classroom A1 |
| 01.12.2026 10:00-14:00 | Grupo /CLIL_03 | Classroom A1 |
| 01.12.2026 10:00-14:00 | Grupo /CLIL_04 | Classroom A1 |
| 01.12.2026 10:00-14:00 | Grupo /CLIL_05 | Classroom A1 |
| 01.12.2026 10:00-14:00 | Grupo /CLE_01 | Classroom A1 |
| 01.12.2026 10:00-14:00 | Grupo /CLIS_03 | Classroom A1 |
| 01.12.2026 10:00-14:00 | Grupo /CLIS_02 | Classroom A2 |
| 01.12.2026 10:00-14:00 | Grupo /CLIL_01 | Classroom A2 |
| 01.12.2026 10:00-14:00 | Grupo /CLIL_02 | Classroom A2 |
| 01.12.2026 10:00-14:00 | Grupo /CLIL_03 | Classroom A2 |
| 01.12.2026 10:00-14:00 | Grupo /CLIL_04 | Classroom A2 |
| 01.12.2026 10:00-14:00 | Grupo /CLIL_05 | Classroom A2 |
| 01.12.2026 10:00-14:00 | Grupo /CLE_01 | Classroom A2 |
| 01.12.2026 10:00-14:00 | Grupo /CLIS_03 | Classroom A2 |
| 01.12.2026 10:00-14:00 | Grupo /CLIS_01 | Classroom A2 |
| 06.19.2026 16:00-20:00 | Grupo /CLIS_01 | Classroom A3 |
| 06.19.2026 16:00-20:00 | Grupo /CLIS_02 | Classroom A3 |
| 06.19.2026 16:00-20:00 | Grupo /CLIL_01 | Classroom A3 |
| 06.19.2026 16:00-20:00 | Grupo /CLIL_02 | Classroom A3 |
| 06.19.2026 16:00-20:00 | Grupo /CLIL_03 | Classroom A3 |
| 06.19.2026 16:00-20:00 | Grupo /CLIL_04 | Classroom A3 |
| 06.19.2026 16:00-20:00 | Grupo /CLIL_05 | Classroom A3 |
| 06.19.2026 16:00-20:00 | Grupo /CLE_01 | Classroom A3 |
| 06.19.2026 16:00-20:00 | Grupo /CLIS_03 | Classroom A3 |