Degree | Type | Year | Semester |
---|---|---|---|
2503852 Applied Statistics | FB | 1 | 1 |
Nothing required.
Have the basic knowledge on Linear Algebra course with emphasize on factorization of matrices: PAQ, P^{-1}AP,P^tAP,SVD-decomposition, and methods for Estadistics: as resolution by linear systems by use in Datta Fitting, generalized inverse matrix, SVD applied to big data.
1. Linear Systems and matrix operations. Operations with matrices. Invertible matrices. Elemental matrix transformations. Gauss-Jordan normal form associated to a matrix. Rang of a matrix. Invertibility criterion. Resolution of linear system equations. Determinants. PAQ-reduction. Inverse generalized matrix.
2. Vector spaces and linear maps: Definition of vector space and examples. Vector structure of R ^ n and subspaces. Definition of linear application and exemples. The Kernel and the image of a linear map. Linear dependence and independence of vectors. Generator systems, Bases of a vector space. Dimension.Coordinates, base change matrices, matrix associated with a linear map fixing basis.
3. Diagonalization of endomorphisms: eigenvectors and eigenvalues of an endomorphism. Character polynomial and minimum polynomial. Diagonalization criteria.
4. Vector spaces with scalar product. Bilinear product, definition and properties. Ortogonality Orthonormal bases. Gram-Schmith ortonormatilization method. Projections Orthogonal Complement. Projection to a subspace. Orthogonal diagonalization of symmetrical matrices, spectral theorem. Data Fitting. Singular values and decomposition in singular values.
Annotation: Within the schedule set by the centre or degree programme, 15 minutes of one class will be reserved for students to evaluate their lecturers and their courses or modules through questionnaires.
Title | Hours | ECTS | Learning Outcomes |
---|---|---|---|
Type: Directed | |||
Lesson | 26 | 1.04 | 5, 3, 4 |
practical lessons with or without Math sources | 26 | 1.04 | 5, 1, 3, 4, 7 |
Type: Supervised | |||
Solving exercises | 40 | 1.6 | 5, 1, 7, 6 |
Type: Autonomous | |||
Learn theoretical concepts | 24 | 0.96 | 5, 3, 4, 7 |
Prepare avaluations | 26 | 1.04 | 5, 1, 3, 4, 7, 2 |
The evaluation of the Linear Algebra course will consist of:
a) Problem solving, "Quiz" type tests 2 points.
b) Computer knowledge test, computer test, Linear Algebra with SageMath or Magma 1.5 points
c) A partial exam 1.5 punts
d) A final exam 5 points.
In case of No positive avaluation (mark lower than 5) there is a single recovery test of sections (c) and (d) of value 6.5 points.
The Linear Algebra course is positive avaluated if one obtain a grade of 5 or higher and obtained a grade higher than 4 in the final exam or in its recovery. (In case of having a grade higher than 5 and a grade lower than 4 in the final exam and recovery exam, the student's grade will be 4.5 points, and will fails the Linear Algebra Course).
It is considered that a student has attended the course (and therefore will be assigned a mark for the Linear Algebra course) if she (or he) has carried out assessment activities that represent a weight equal to or greater than 50% of the final grade of the subject.
Title | Weighting | Hours | ECTS | Learning Outcomes |
---|---|---|---|---|
Solving exercises | 15 | 1 | 0.04 | 5, 3, 4, 7, 6 |
Work with Sage Math | 15 | 1 | 0.04 | 3, 4, 2 |
Writting exams | 70 | 6 | 0.24 | 5, 1, 3, 4, 6, 2 |
Basic Bibliography:
Otto Bretscher: Linear Algebra with Applications. Pearson Prentice Hall, 3er edition.
Enric Nart,Xavier Xarles: Apunts d'àlgebra lineal,Material UAB, 237 (2016), UAB.
Additional Bibliography:
Stanley I. Grossman, Álgebra lineal, Grupo Editorial Iberoamérica, 1983.
Shayle R. Searle, Matrix Algebra Useful for Statistics, Wiley-Interscience
David A. Harville, Matrix Algebra from a Statistician's Perspective, Springer
Virtual Bibliografy:
F.Bars, Uns apunts Uns apunts de càlcul matricial i resolució de sistemes lineals https://ddd.uab.cat/record/73660
F.Bars, Una pinzellada al polínomi mínim; https://ddd.uab.cat/record/236746
F.Bars, Espais normats i espais de Hilbert per a primer curs, https://ddd.uab.cat/record/236744?ln=ca
We use Sage Math programme during some lessons.