Linear Algebra


In this curricular unit we intend that the students develop their habilities in logic thought and calculus, essential for other curricular units. The main goal is learning the fundamentals of Linear Algebra.

General characterization





Responsible teacher

Patrícia Santos Ribeiro


Weekly - Available soon

Total - Available soon

Teaching language

Portuguese. If there are Erasmus students, classes will be taught in English


There are no requirements


Lay, D., Linear Algebra and its applications, 3rd ed., Pearson Education, 2006.; Sydsæter, K, Hammond, P., Essential Mathematics for Economic Analysis, 2nd ed., Prentice Hall, 2006.; Giraldes, E., Fernandes, V. H. e Smith, M. P. M, Curso de Álgebra Linear e Geometria Analítica, Editora McGraw-Hill de Portugal, 1995. ; Cabral, I., Perdigão, C., Saiago, C., Álgebra Linear, Escolar Editora, 2008.; Monteiro, A., Pinto, G. e Marques, C., Álgebra Linear e Geometria Analítica (Problemas e Exercícios), McGraw-Hill, 1997.

Teaching method

Lectures and practical classes in order to solve exercises

Evaluation method

Continue evaluation: 
2 tests during the semester (minimum grade: 9,5 points)Final classification: average of the two tests.

Exam Evaluation (only in 2nd season):
Final Exam (100%) (minimum grade: 9,5 points)

Subject matter

1. Vector Spaces
1.1. Dependence and linear combination of vectors.
1.2. Vector Subspaces.
1.3. Base and dimension of a vector space.
2. Matrices
2.1. Definition and classification of matrices.
2.2. Operations between matrices.
2.3. Caracteristic of a matrix; Inverse of a matrix.
3. Determinants
3.1. Calculation and proprieties of determinants.
3.2. Minors and algebric complements.
3.3. Adjoint matrix.
4. Sistems of linear equations
4.1.Definition, matrix representation and resolution of a sistem linear equation
4.2. Calculation of the adjoint matrix using the condensation method
5. Eigenvalues and Eigenvectors
5.1. Definition.
5.2. Caracteristic polynomial and Caracteristic equation.
5.3. Main Results.
6. Introduction to quadratic forms