Linear Algebra

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.

Perform the basic operations of matrix calculus. Calculate determinants, eigenvalues and eigenvectors. Understand and apply the concepts related to vector spaces and linear transformations. Solve and interpret systems of linear equations using matrices and their properties. Understand the importance of linear algebra in computer science and computer engineering. Recognize the importance of algorithms in linear algebra. Solve practical problems involving matrices and linear systems. Develop algorithms using logical and structured reasoning. Select, in an appropriate manner, information accessible through various media (books, journals, internet, etc.). Present the resolution of problems in a clear and concise manner.

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

Main Bibliography

• Anton, H. & Rorres, C. (2005). Elementary Linear Algebra with applications. (9ª ed.). John Wiley & Sons. Cota Biblioteca: 3-1-99 (ISEC) – 11300;
• Cabral, I., Perdigão, C. & Santiago, C. (2018). Álgebra Linear – Teoria, Exercícios resolvidos e Exercícios propostos com soluções. (5ª ed.). Escolar Editora. Cota Biblioteca:  3-1-27 (ISEC) – 15011;
• Fidalgo, C. (2016). Álgebra Linear, DFM, Instituto Superior de Engenharia de Coimbra. Cota Biblioteca: 3-1-116 (ISEC) – 13179;
• Graham, A. (2018). Matrix Theory and Applications for Scientists and Engineers. Dover Books on Mathematics. Cota Biblioteca: 3-1-58 (ISEC) – 03750;
• James, G. & Dyke, P. (2020). Modern Engineering Mathematics. (6ª ed.). Pearson. Cota Biblioteca: 3-2-193 (ISEC) – 08334, 3-2-220 (ISEC) – 08838, 3-2-221 (ISEC) – 08839;
• Kreyszig, E. (2011). Advanced Engineering Mathematics (10ª ed.). John Wiley & Sons. Cota Biblioteca: 3-7-95 (ISEC) – 17207, 3-7-51 (ISEC) – 11749, 3-7-52 (ISEC) – 11750, 3-7-53 (ISEC) – 11751;
• Monteiro, A., Marques, C. & Pinto, G. (2000). Álgebra Linear e Geometria Analítica. Problemas e Exercícios. McGraw-Hill. Cota Biblioteca: 3-1-75 (ISEC) – 08697, 3-1-76 (ISEC) – 08698.

Complementary Bibliography

• Nicholson, W. (1993). Elementary Linear Algebra with Applications. (2ª ed.). PWS Publishing Company;
• Santana, A. & Queiró, J. (2018). Introdução à Álgebra Linear. Gradiva.