# Linear Algebra

## Objectives

The general objectives are to provide students with fundamental tools of Linear Algebra, in view of its future use as an auxiliary instrument in different disciplines of Information Management.

## General characterization

100001

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

The student must have successfully completed an high-school course in calculus, with the usual requirements considered within the European Union.

### 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

The teaching method relies on weekly theoretical lectures and practical classes, supported by an attending schedule. Practical examples are provided in the theoretical lectures. Exercises are solved under teacher supervision in the practical classes.

### Evaluation method

The continuous evaluation method consists in two tests. The student is approved if the average of the two grades is upper or equal to 9.5.

Note: The student may optionally improve the grade of the first test at the date of the second test.

The non-approved student in continuous evaluation must attend the final exam, being aproved if the grade is upper or equal to 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. Characteristic of a matrix; Inverse of a matrix.

3. Determinants.

3.1. Calculation and proprieties of determinants.

3.2. Minors and algebraic complements.

4. Systems of linear equations.

4.1. Definition, matrix representation and resolution of a system linear equation.

4.2. Calculation of the adjoint matrix using the condensation method.

5. Eigenvalues and Eigenvectors.

5.1. Definition.

5.2. Characteristic polynomial and characteristic equation.

5.3. Main results.