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Linear Algebra

Objectives

In this curricular unit it is intended that students develop algebraic skills, namely algorithmic conception, computional efficiency and inference of abstract structures of real models. Closely connected to the efficient organization of large amounts of numerical data, Linear Algebra  will be a fundamental knowledge to other curricular units of the academic studies in Information Management. 

General characterization

Code

100001

Credits

4.0

Responsible teacher

José António da Silva Carvalho

Hours

Weekly - Available soon

Total - Available soon

Teaching language

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

Prerequisites

There are no requirements

Bibliography

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