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Prerequisites
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Duration
Identical coursesAims
The students become familiar with the following aspects of linear algebra, which together form an important mathematical basis for future courses:
- matrix computations
- solving linear systems of equations
- basic algebraic concepts and methods that are used in data analysis applications
- links between vector space representations and matrices, and between decompositions such as eigenvalue decomposition, singular value decomposition, linear systems, least squares solutions
At the end of this course, students should:
- understand basic theoretical concepts of linear algebra, apply them, and integrate them
- be able to use algebraic methods and tools to solve mathematical problems
- be able to transform a descriptive problem into a mathematical formulation, and to identify the algebraic method(s) that can be used to solve them
Previous knowledge
High-school mathematics.
Is included in these courses of study
- Master of Geography (Programme for students started before 2021-2022) (Leuven et al) (CITY, SOCIETY AND SPACE) 120 ects.
- Master of Geography (Programme for students started before 2021-2022) (Leuven et al) (EARTH AND CLIMATE) 120 ects.
- Master of Geography (Programme for students started before 2021-2022) (Leuven et al) (GIS AND SPATIAL MODELLING) 120 ects.
- Master of Bioinformatics (Leuven) 120 ects.
- Courses for Exchange Students Faculty of Bioscience Engineering (Leuven)
- Master of Bioscience Engineering: Human Health Engineering (Leuven) 120 ects.
- Master of Bioscience Engineering: Agro- and Ecosystems Engineering (Leuven) 120 ects.
- Master of Bioscience Engineering: Cellular and Genetic Engineering (Leuven) 120 ects.
- Master of Geography (Programme for students started in 2021-2022 or later) (Leuven et al) 120 ects.
Activities
6 ects. Linear Algebra (B-KUL-I0D38a)
Content
- Systems of linear equations, row echelon form, rank of a matrix
- Matrix algebra and determinants
- Vector spaces
- Eigenvalues and eigenvectors, matrix diagonalisation
- Norms, distances, inner product
- Orthogonal projection, projection matrix
- Gram-Schmidt orthogonalisation, QR
- Singular value decomposition, generalised inverse, best rank k approximation
- Least squares solution
- Principal Component Analysis
Course material
- Textbook: David C. Lay, Linear Algebra and its Applications, 5th (or 4th) edition, Pearson Education
- Slides (on Toledo)
- Material for exercise sessions (on Toledo)
Language of instruction: more information
This course will be taught in English
Format: more information
Theoretical concepts in linear algebra are taught and then applied in different examples.
The chapters in the textbook which are supposed to be known for the exam will be given during the first lecture, and will be listed on Toledo (see slides of first lecture).
Students are expected to study the theoretical concepts from the text book (at home) before a lecture, and stay up to date with the material that has been covered in the lectures. During the contact moments, the students should be able to interact with the lecturer and with their peers based on what they have studied. During the lectures, some time is reserved for discussion (Q&A). A limited amount of material is self-study and will not be covered in the lectures.
The lectures are complemented with exercise sessions (pen and paper)
1 ects. Exercises in Linear Algebra (B-KUL-I0D91a)
Content
Systems of equations and the echelon form, Rank and null space of a matrix, Determinants, Inverse, QR decomposition, Characteristic polynomial, Eigenvalue decomposition, Singular value decomposition, Least Squares, Principal Component Analysis
Course material
List of exercises on Toledo
Format: more information
Exercises are solved in small groups. A TA will be available during the exercise session to ask questions or request assistance. Some exercises are also solved with the whole class together. The exercise sessions are only useful if the students have studied the relevant chapter in the handbook beforehand. During the exercise sessions there is also the possibility to clarify concepts or exercises that were explained during the lectures.
Is also included in other courses
Evaluation
Evaluation: Linear Algebra (B-KUL-I2D38b)
Explanation
Written examination with exercises:
The students can use the text book of Lay (Linear Algebra and its Applications), but nothing else (no personal papers with summary, exercises, slides, etc.). A simple calculator with only digits display can be used (no graphical calculator and no calculators that can perform matrix calculations!).
It is important to give sufficient in-between steps in the mathematical derivations/calculations, and to clearly explain the reasoning that leads to the solution. Missing steps and giant leaps in the calculations/derivations, while still reaching the right solution, will be treated as 'suspicious' (e.g., the illegal use of a calculator or software that can perform matrix calculation, etc.)
The students can take a mock exam during the semester of which the grade is scaled to a grade x/1. Students who pass this mock exam, meaning they have scored at least 0.5/1 for this exam, will have this grade added as a bonus to the grade of their final exam. Participation in this mock exam is not mandatory: students can still obtain the maximum grade for the final exam without participating in the mock exam.
Information about retaking exams
The score of the mock exam is not added to the grade of the retake exam.