Description

Theory
2

Theory/Practice
2

Instructors

Ana Cristina Meira

Contents

1. Complex numbers
 

2 Matrix calculus and Determinants (6 weeks, 40%)
2.1 Notation and classification
2.2 Algebraic operations with matrices
2.3 Operations on matrices
2.4 Matrices equations
2.5 Determinants of a matrix
2.6 Inverse of a matrix
2.7 Powers of matrices
 

3. Systems of linear equations (3 weeks, 20%)
3.1 Notations and classification
3.2 Systems solving by Gaussian elimination and Crammer methods.
3.3 Discussion of systems with parameters.
 

4. Vector spaces (3 weeks, 20%)
4.1 Definition and properties.
4.2 Vector subspace
4.3 Linear combination of vectors. Linear dependence and independence of vectors
4.4 Base and dimension of a vector space
4.5 Matrix for a change of base
4.6 Vector spaces with inner product
 

5 Linear transforms from Rn to Rm (3 weeks, 20%)
5.1 Definition and classification
5.2 Kernel and image of a L.T.
5.3 Algebra of a L.T. matrix
5.4 Eigenvalues and eigenvectors

Learning Outcomes

i) Provide students with basic language, concepts, and methods of Linear Algebra related to matrix calculus and determinants, systems of linear equations, vector spaces, and linear transforms;
ii) Promote the development of the student?s reasoning, critical spirit, mathematical thinking, and rigor in argumentation;
iii) Promote the development of the student's capacity for abstraction, structuring of problems, and the attempt to solve them;
iv) Provide the student with such skills that, based on the knowledge acquired, enable him, intuitively, to solve and to implement computationally problems presented in other courses along with the graduation.