Objectives and Contextualisation
This is a basic introduction to linear algebra, emphasizing the most functional and instrumental aspects of linear techniques.
A fundamental objective is to achieve an agile and efficient transition between the three following levels of knowledge:
Abstract knowledge of mathematical concepts related to linear phenomena.
Deepened knowledge of the same concept from its practical manipulation "by hand".
Deepened knowledge of the same concept from its practical manipulation with a computer.
The most important fundamental objective is to learn to design efficient strategies to apply specific techniques to solve
complex problems.
Competences
Electronic Engineering for Telecommunication
Communication
Develop personal work habits.
Learn new methods and technologies, building on basic technological knowledge, to be able to adapt to new situations.
Perform measurements, calculations, estimations, valuations, analyses, studies, reports, task-scheduling and other similar work in the field of telecommunication systems
Work in a team.
Telecommunication Systems Engineering
Develop personal work habits.
Develop thinking habits.
Learn new methods and technologies, building on basic technological knowledge, to be able to adapt to new situations.
Learning Outcomes
Analyse measurements in the area of engineering, using statistical tools to extract and understand information.
Analyse measures in the area of engineering, using statistical tools to extract and understand information.
Apply, in the problems that arise in engineering, knowledge about linear algebra, geometry, differential geometry, differential and integral calculus, differential and partial derivative equations, numerical methods, numerical algorithms, statistics and optimisation.
Apply, to the problems that arise in engineering, knowledge of linear algebra, geometry, differential geometry, differential and integral calculus, differential and partial derivative equations, numerical methods, numerical algorithms, statistics and optimisation.
Communicate efficiently, orally and in writing, knowledge, results and skills, both professionally and to non-expert audiences.
Develop scientific thinking.
Develop the capacity for analysis and synthesis.
Manage available time and resources.
Model systems and analyse their features.
Resolve the mathematical problems that can arise in engineering.
Work autonomously.
Work cooperatively.
Content
Matrices
Matrices. Operations with marices. Special matrices: symmetric, Toeplitz, circulant, invertible, hermitian, orthogonal.
Elemental transformations by rows. Gauss-Jordan's normal form of a matrix. Rank of a matrix. Invertibility and calculation of inverse matrices.
Systems of linear equations and linear varieties. Gauss method. Direction and dimension of linear varieties. Rouché's Theorem.
Vector Spaces
Definition of vector space and examples. Linear combinations of vectors. Subspaces. Generating systems.
Linear maps. Matrix associated to a linear map. Composition of linear maps. Kernel and Image of a linear map. Isomorphisms.
Linear dependence of vectors. Linear dependence criterion.
Bases, dimensions and coordinates. Working with coordinates. Base changes.
Diagonalization of matrices and inner products.
Determinant of a square matrix. Properties of the determinant.
Eigenvalues and eigenvectors of a square matrix. Diagonalization criteria.
Applications of diagonalisation: calculation of matrix powers and resolution of systems of linear differential equations with constant coefficients.
