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
Não é previamente marcado um horário de atendimento do aluno. Sempre que o aluno, individualmente ou em grupo, sinta necessidade de apoio é agendado um horário para os receber.