Álgebra Linear

Main properties of the real number system and the complex number system (taught in high school mathematics subjects)

Theoretical classes consist of a detailed exposition of each subject that is immediately complemented by the resolution of exercises. In the theoretical-practical classes it is intended that the student solves application exercises with the guidance of the teacher.

Objectives: To provide students with basic knowledge of Linear Algebra, with a view to easy application of the discipline in the most diverse fields of Engineering.

Skills: Development of mathematical abstraction and logical reasoning, as well as identification, understanding and solving problems involving matrix calculus (matrices, linear systems, determinants), vector spaces and eigenvalues and eigenvectors (diagonalization of matrices).

CHAPTER I – Reviews on complex numbers
CHAPTER II – Matrices

     Definitions

     Operations with matrices and properties

CHAPTER III – Systems of Linear Equations

     Condensation of matrices and characteristic

     Systems of linear equations

     Classification and solution of systems of linear equations by condensation

     Inverse matrix

CHAPTER IV – Determinants

     Definitions, evaluation and Properties

     Laplace’s Theorem

     Cramer’s Rule

CHAPTER V – Vector Spaces

     Definitions and examples

     Vector subspaces

     Vector subspace generated by a set of vectors

     Linear dependence and independence

     Basis and dimension

CHAPTER VI – Eigenvalues and Eigenvectors

     Definitions, computation and properties

     Diagonalization

     Cayley-Hamilton Theorem

NAO

• Anton, H. & Rorres, C. (2005). – Elementary Linear Algebra with applications. (9ª ed.). John Wiley & Sons.
• Cabral, I., Perdigão, C. & Santiago, C. (2018). Álgebra Linear – Teoria, Exercícios resolvidos e Exercícios propostos com soluções. (5ª ed.). Escolar Editora.
• Fidalgo, C. (2016). – Álgebra Linear, DFM, Instituto Superior de Engenharia de Coimbra.
• Graham, A. (2018). Matrix Theory and Applications for Scientists and Engineers. Dover Books on Mathematics
• James, G. & Dyke, P. (2020). Modern Engineering Mathematics. (6ª ed.). Pearson.
• Kreyszig, E. (2011). Advanced Engineering Mathematics (10ª ed.). John Wiley & Sons.
• Monteiro, A., Marques, C. & Pinto, G. (2000). Álgebra Linear e Geometria Analítica. Problemas e Exercícios. McGraw-Hill.
• Nicholson, W. (1993). Elementary Linear Algebra with Applications. (2ª ed.). PWS Publishing Company.
• Santana, A. & Queiró, J. (2018). Introdução à Álgebra Linear. Gradiva.