ECTS credits ECTS credits: 6
ECTS Hours Rules/Memories Student's work ECTS: 99 Hours of tutorials: 3 Expository Class: 24 Interactive Classroom: 24 Total: 150
Use languages Spanish, Galician, English
Type: Ordinary Degree Subject RD 1393/2007 - 822/2021
Center Faculty of Mathematics
Call: Second Semester
Teaching: Sin Docencia (En Extinción)
Enrolment: No Matriculable (Sólo Planes en Extinción)
Linear Algebra is an essential part of the mathematical toolkit required in the modern study of many areas of behavioral, natural, physical and social sciences, in engineering, in business, in computer science, and of course in pure and applied mathematics.
The purposes of this course is to develop the basic concepts of linear algebra and to illustrate their usability by means of a variety of selected applications. More precisely, one can say that the aims are:
i) To provide a first contact with algebraic structures: vector spaces and linear maps as a generalization of vectors in R^3 and matrices, respectively. To learn how to operate with vectors, basis, subspaces and linear maps.
ii)To get acquaintance with the use of matrices in different branches of knowledge.
iii) To understand the need for reducing matrices to predetermined forms and to practice the algorithms.
1.- Vector spaces. (5 theoretical hours)
Definition of vector space: Examples. Subspaces. Quotient spaces. Intersection and sum of subspaces. Systems of generators .
2.- Linear independence and dimension. (6 theoretical hours)
Linear dependence and independence. Bases and dimension. Equations for a subspace. Coordinates. Supplementary subspaces.
3.- Applications between vector spaces. (9 theoretical hours)
Definition of linear map: properties and examples. Subspaces associated to a linear map. The vector space of linear maps. Matrix of a linear map. Change of basis and linear maps.
4.- Matrices. (5 theoretical hours)
Operations with matrices and properties. Non singular matrices. Elementary matrices. Equivalent matrices. Rank of a matrix.
5.- Systems of linear equations. (3 theoretical hours)
Systems of linear equations. Gaussian elimination. The Rouché-Frobenius Theorem.
Basic.
1.-Cohn, P. M. Algebra, Vol. 1(2ª Ed.). Wiley and Sons, Chichester, 1982.
2.-Jeronimo, G., Sabia, J., Tesauri, S. Álgebra lineal. http://mate.dm.uba.ar/~jeronimo/algebra_lineal/AlgebraLineal.pdf.
3.-López Camino, Rafael. Apuntes Geometría I. Curso 2003-2004. Universidad de Granada.
https://www.ugr.es/~rcamino/docencia/geo1-03/g1tema1.pdf
https://www.ugr.es/~rcamino/docencia/geo1-03/g1tema2.pdf
https://www.ugr.es/~rcamino/docencia/geo1-03/g1tema3.pdf
Complementary
1.-Bolos, J.; Cayetano, J.; Requejo, B. Álgebra lineal y Geometría. UNEX, 2007.
2.-Merino, L.; Santos, E. Álgebra lineal con métodos elementales. Thomson, 2006.
Contribute to achieving the basic, general and transversal competences included in the report of the Degree in Mathematics of the USC: CB1, CB2, CB3, CB4, CB5, CG1, CG2, CG3, CG4, CG5, CT1, CT2, CT3, CT5.
Know the basic concepts of Linear Algebra.
Know the algorithms to reduce matrices to row-echelon forms and know how to apply them to the calculation of the range, calculation of base, resolution of systems, etc.
Understand the close relationship between matrices, linear applications and systems of linear equations and be able to use them in different contexts.
without teaching
Final exame grade
without teaching
Rosa Mª Fernandez Rodriguez
- Department
- Mathematics
- Area
- Algebra
- Phone
- 881813158
- rosam.fernandez [at] usc.es
- Category
- Professor: University Lecturer
| 05.18.2026 10:00-14:00 | Grupo de examen | Classroom 06 |
| 07.01.2026 16:00-20:00 | Grupo de examen | Classroom 06 |