# Linear Algebra

## Objectives

In this curricular unit it is intended that students develop their logical reasoning and calculation skills, essential for the learning of other curricular units of their cycle of studies. The main goal is the learning and consolidation of fundamental knowledge of Linear Algebra.

## General characterization

100001

4.0

##### Responsible teacher

Patrícia Santos Ribeiro

##### 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.

Strang, G., Linear Algebra and its Applications, Hartcourt Brace Jonovich Publishers, 1998

### Teaching method

Lectures and practical classes in order to solve exercises

### Evaluation method

Continuous Assessment (1st period)

The continuous assessment consists of conducting, during the academic semester, two tests (minimum grade on each test: 9,5).

Final grade: Average of the two tests

If, exceptionally, it is not possible to have a test or an exam in person, it will be conducted online followed by an oral test, but the situation will be analyzed on a case-by-case basis.

Exam Assessment (only 2nd period)

Final Exam (100%) (face-to-face, minimum score: 9,5)

## 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

## Programs

Programs where the course is taught: