In this subject, the concepts of linear algebra necessary to develop the analysis of data and their visualization throughout the Bachelor's degree will be introduced. We will study algebraic concepts from the point of view of matrix algebra, but also from the geometrical and numerical. Emphasis will be placed on examples from the field of computing, data modelling, and image processing.
Person in charge
Anna Rio Doval (
Jordi Guardia Rubies (
Josefina Antonijuan Rull (
Marta Casanellas Rius (
CE1 - Skillfully use mathematical concepts and methods that underlie the problems of science and data engineering.
CT5 - Solvent use of information resources. Manage the acquisition, structuring, analysis and visualization of data and information in the field of specialty and critically evaluate the results of such management.
CT6 - Autonomous Learning. Detect deficiencies in one's own knowledge and overcome them through critical reflection and the choice of the best action to extend this knowledge.
CB1 - That students have demonstrated to possess and understand knowledge in an area of ??study that starts from the base of general secondary education, and is usually found at a level that, although supported by advanced textbooks, also includes some aspects that imply Knowledge from the vanguard of their field of study.
Generic Technical Competences
CG2 - Choose and apply the most appropriate methods and techniques to a problem defined by data that represents a challenge for its volume, speed, variety or heterogeneity, including computer, mathematical, statistical and signal processing methods.
Acquisition of the basic knowledge of linear algebra (vector spaces, matrices, linear systems)
Recognize concepts of linear algebra within interdisciplinary problems.
Learn how to use linear algebra in solving problems of data analysis and modeling.
Using linear algebra tools in mathematical problems
Using software to solve exercises related to linear algebra
Understanding of the notions of matrix decomposition, its geometric interpretation and its application in exercise solving
Definition and operations with metrices, rank, elementary transformations.
Gaussian elimination, discussion of solutions of linear systems, numerical methods for linear system solving. Linear systems in data modelization.
Vector space definition. Vectors, linear combinations, dependency, generators, bases, coordinates. Vector subspaces, intersection and sum.
Linear maps, kernel and range, rank; matrix of a linear map in a basis; change of basis
Eigenvalues and eigenvectors; characteristic polynomial; algebraic and geometric multiplicity, diagonalization criteria, application to the computation of power of matrices and functions of matrices. Special case of Markov matrices and symmetric matrices.
Linear discrete dynamical systems
Madelling of problems via linear discrete dynamical systems, resolution and analysis of particular and generic solutions; long.term behaviour of hte solutions; numerical methods for the computation of eigenvalues and eigenvectors; recurrencies and homogeneous linear difference equations, resolution and study of the solutions.
Inner product, norm, distance, angle; orthogonal complement and orthogonal projection; orthonormal basis and orthogonalization methods; orthogonal matrices and isometries; matrix norm; singular value decomposition, application to rank approximation and dimensional reduction in data and image analysis; bilinear and quadratic forms; spectral theorem and inertia indices.
Development of topic 1
Classes de teoria i de problemes corresponents al tema 1 Objectives:152 Contents:
Different methodologies will be considered for lectures and exercises classes.
The lectures will consist mainly of master classes, based on presentations and explanations on the slate; the problem classes will be to solve exercises and practice concepts learned in the theory sessions.
Both of them may incorporate examples o short projects using python or similar software.
The assessment of the subject will consist of the marks: P, F, L
The mark P will be obtained from the partial exam.
The mark F will be obtained from the final exam.
The mark L will be obtained by evaluation of problem resolution using python or another software.
The final mark will be computed as follows:
Note = maximum (60% F + 30% P + 10% L, F)
The re-evaluation grade will be the mark of the reavaluation exam.