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IPLUSO 2091

Linear Algebra

Computer Engineering and Applications
  • ApresentaçãoPresentation
    In an Engineering study cycle, curricular units in the scientific area of ¿¿Mathematics play an important role. They are essential for students to acquire solid basic knowledge needed in other curricular units of the study cycle that require mathematical knowledge or new skills and competences acquired through gradual and persistent work in curricular units in this area. The curricular unit of Linear Algebra assumes a fundamental and relevant role in the beginning of students' mathematical training. Mathematical contents are essential in the training of qualified staff, either in the understanding and consolidation of the different concepts, or in the specific knowledge of their applicability and in the development of new skills and competences acquired with the work in the curricular unit. Much of the content explored in some topics of the mentioned syllabus has a wide application in other areas of the study cycle.
  • ProgramaProgramme
    1. Number sets. Complex numbers. Operations in algebraic form. 2. Arrays. Types of Arrays. Properties. matrix algebra 3. Characteristics and condensation of matrices. Rouche's Theorem. Linear dependence and independence. 4. Invertible matrices. 5 Systems of linear equations. Resolution and discussion. 6. Elementary matrices. permutations. Determinant and properties 7. Complementary minors and assistant. Laplace's Theorem. Cramer's Rule. 8. Vectors and eigenvalues (VVPs). Invariants. Characteristic polynomial. 9. Diagonalization of matrices. Jordan block and canonical form. 10. Vector spaces. Subspaces. Basis and dimension 11. Linear transformations. Injectivity and surjectivity. Image and core. Matrix of a linear application 12. Vector spaces with inner product. External product and mixed product.
  • ObjectivosObjectives
    At the general objective level, it is intended to familiarize students with the fundamental concepts of Linear Algebra and with abstract reasoning in general. In specific terms, after addressing the syllabus, tasks and exercises are proposed to apply the concepts explored with the consequent diversity of contexts in which they can be applied in the field of engineering in general. In particular, mastering the main techniques of matrix calculus, calculus of determinants and applications, calculus of vectors and eigenvalues and vector calculus that can be used to solve different problems in the horizon of technologies and engineering and, in particular, of computer engineering.
  • BibliografiaBibliography
    Simões, Vasco - Álgebra Linear. 1ª Edição. Lisboa: Edições Orion. 2013. ISBN: 978 972 862 0240 Cabral, I., Perdigão, C., Saiago C. - Álgebra ¿ Teoria e Exercícios. 1ª Edição. Lisboa: Escolar Editora. 2009. ISBN: 978 972 592 239 2 Magalhães, L. T. , Álgebra Linear como introdução à Matemática Aplicada, Texto Editora, 2001 Monteiro, A.; Pinto, G. (1997). Álgebra Linear e Geometria Analítica. Problemas e exercícios, McGraw-Hill. 
  • MetodologiaMethodology
    Possibility of using appropriate software to carry out certain tasks
  • LínguaLanguage
    Português
  • TipoType
    Semestral
  • ECTS
    6
  • NaturezaNature
    Mandatory
  • EstágioInternship
    Não