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  • Linear Algebra

Universidade Lusófona

Linear Algebra

Presentation

In the sequence of Mathematics Discrete, the Algebra Linear is a discipline of the 2nd semester of the course and studies the vector spaces that are finitely generated. The vector spaces studied are on prime fields or on the field of real numbers

The study of vector spaces gives students competence to analyze problems, equate them and define diversified resolution strategies.

 

Linear applications lead to the concept of a matrix that appears as a calculation tool in the study of vector spaces.

 

The student acquires some techniques of matrix calculus and gives the set of the finite matrices the structure of vectorial space.

 

The student has the opportunity to establish an isomorphism between matrix vector spaces and the vectorial space of linear applications which will allow him to select, in the resolution of problems, the space where to work taking into consideration the specificity of the respective problem.

Part of this Programme

Computing Engineering

Level of Qualification|Semesters|ECTS

| Semestral | 5

Year | Type of course unit | Language

1 |Mandatory |Português

Code

ULHT260-2091

Recommended complementary curricular units

Although one does not recommend any particular discipline, it is considered that it would be interesting for the student have an introductory course of  Theory of Fields

Prerequisites and co-requisites

n/a

Professional Internship

Não

Syllabus

Brief apresentation of the field of real numbers. Brief introduction to the Zp fields

 

Real vector spaces: Subspaces . Steinitz theorem and its consequences

 

Linear maps. Isomorphisms

 

Real Matrices: Matrix vector spaces. Product of matrices

 

Systems of linear equations: Study  and resolution of systems of linear equations. Representation        of subspaces through systems of linear equations

Determinants: Properties of       determinants . Theorem of La Place

 

Eigen values and eigen vectors.

Objectives

To understand the structure of vector space. To understand the concept of linear map and its properties. To operate inside matrix spaces. To be familiar with the theory of determinants and to apply it in the resolution of problems. To recognize the importance of matrix diagonalization. This curricular unit provides competences which allow using previously acquired knowledge towards a better definition of strategy when solving problems. The student will develop deductive and analytical reasoning related

competences. The student will further develop the capacity to deal with the several characterizations of a given concept and the competence to select the appropriate information in each situation.

Teaching methodologies and assessment

The exposition of subjects is done with the active participation of students. Some concrete examples are shown and the students are invited to analyze the concepts at stake in each example, thus appearing, in

a natural way, the definitions and corresponding propositions.

 

Evaluation comprises a continuous component which includes active participation in classes and 4 homework assignments weighting 40% of the final classification. A final written test takes place at the end of the semester weighting 60%. Students having more than 16 may have to perform and extra test, the non performance of which yield a final mark of 16.

References

Almada, T.; Álgebra Linear , Edições Universitárias Lusófonas, 2007.

Pires dos Santos, J.M.; Tópicos de Álgebra Linear , J. M., AEFCUL, 1995.

Magalhães, L. T. ; Álgebra Linear como introdução à Matemática Aplicada , Texto Editora, 2001. Almada, T.; Elementos de Álgebra Linear , Sebenta, Edições Universitárias Lusófonas, 2008.

 

Office Hours

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Saiba como realizar a sua candidatura como Aluno Externo para Frequência de unidades curriculares avulso na Universidade Lusófona.

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