Course: 2023/2024

Linear Geometry

(18259)

Requirements (Subjects that are assumed to be known)

Fundamentals of Algebra,
Linear Algebra,
Differential Calculus

Skills and learning outcomes

Description of contents: programme

1. Bilinear and quadratic forms
2. Positive definite matrices
3. Least squares problems
4. Eigenvalues and eigenvectors: diagonalization of matrices and Schur's triangularization
5. The Jordan canonical form
6. Normal matrices and their spectral theorem
7. The singular value decomposition
8. Affine spaces and their applications
9. Conic sections and quadric surfaces

Learning activities and methodology

LEARNING ACTIVITIES AND METHODOLOGY
THEORETICAL-PRACTICAL CLASSES. [44 hours with 100% classroom instruction, 1.76 ECTS]
Knowledge and concepts students must acquire. Student receive course notes and
will have basic reference texts to facilitate following the classes and carrying
out follow up work. Students partake in exercises to resolve practical problems
and participate in workshops and evaluation tests, all geared towards
acquiring the necessary capabilities.
TUTORING SESSIONS. [4 hours of tutoring with 100% on-site attendance, 0.16 ECTS]
Individualized attendance (individual tutoring) or in-group (group tutoring) for students with a teacher.
STUDENT INDIVIDUAL WORK OR GROUP WORK [98 hours with 0 % on-site, 3.92 ECTS]
FINAL EXAM. [4 hours with 100% on site, 0.16 ECTS]
Global assessment of knowledge, skills and capacities acquired throughout the course.
METHODOLOGIES
THEORY CLASS. Classroom presentations by the teacher with IT and audiovisual
support in which the subject`s main concepts are developed, while providing
material and bibliography to complement student learning.
PRACTICAL CLASS. Resolution of practical cases and problems, posed by the
teacher, and carried out individually or in a group.
TUTORING SESSIONS. Individualized attendance (individual tutoring sessions) or
in-group (group tutoring sessions) for students with a teacher as tutor.

Assessment System

- % end-of-term-examination 50
- % of continuous assessment (assigments, laboratory, practicals...) 50

Basic Bibliography

- B. Noble, J.W. Daniel. Applied Linear Algebra. Prentice-Hall Int.. 1988
- C.D. Meyer. Matrix Analysis and Applied Linear Algebra. SIAM. 2000
- D.C. Lay, S.R. Lay, J.J. McDonald. Linear Algebra and its Applications. 5th edition. Pearson, 2016
- G. Strang. Introduction to Linear Algebra. Wellesley-Cambridge Press. 2016
- O. Faugeras. Three Dimensional Computer Vision, A Geometric Viewpoint. The MIT Press. 1993
- S.R. García and R.A. Horn. A Second Course in Linear Algebra. Cambridge University Press. 2017

- David Lay, Steven Lay, and Judi McDonald · Linear Algebra and Its Applications, EBook, Global Edition : https://ebookcentral.proquest.com/lib/bibliouc3m-ebooks/detail.action?pq-origsite=primo&docID=5174425

Additional Bibliography

- E. Outerelo Domínguez y J.M. Sánchez Abril. Nociones de Geometría Proyectiva. Sanz y Torres. 2009
- P. Lancaster and M. Tismenetsky. The Theory of Matrices with Applications, 2nd edition. Academic Press, Inc.. 1985
- R.A. Horn and C.R. Johnson. Matrix Analysis, 2nd edition. Cambridge University Press. 2013

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The course syllabus may change due academic events or other reasons.