Course - Linear Algebra with Applications - MA1202
MA1202 - Linear Algebra with Applications
About
Examination arrangement
Examination arrangement: School exam
Grade: Letter grades
| Evaluation | Weighting | Duration | Grade deviation | Examination aids |
|---|---|---|---|---|
| School exam | 100/100 | 4 hours | D |
Course content
The course is a continuation of MA1201. We start with general vector spaces over the real and complex numbers, and linear maps (including related subspaces kernel and image and representations in matrix form given bases). We study operators on finite dimensional vector spaces by looking at eigenvectors, eigenspaces, generalized eigenspaces, aiming for the Cayley-Hamilton theorem and normal forms. Inner product spaces are a concept generalizing the dot product. Studying these, both over the real and complex numbers, is an important part of this course. Orthogonal bases are constructed by using the Gram Schmidt algorithm. Then various types of operators on inner product spaces are studied (orthogonal, real symmetric, unitary, normal, self-adjoint), including the corresponding matrices. The course can contain more advanced concepts from linear algebra, such as dual spaces, bilinear forms and quotient spaces. Several applications are illustrated; these may vary from year to year. Examples: Markov chains, population growth (Leslie matrices), game theory, systems of differential equations, Fourier analysis, and fractals.
Learning outcome
1. Knowledge. The student is familiar with basic concepts concerning general vector spaces, matrices and linear transformations as discussed above. The student is familiar with several applications of linear algebra. 2. Skills. The student masters various algorithms and methods to make calculations involving vector spaces, inner product spaces, and linear transformations. Central skills are applying the Gram-Schmidt algorithm, finding eigenspaces, diagonalizing matrices, and applications varying from year to year. The student is able to write simple mathematical proofs.
Learning methods and activities
Lectures and exercises. Parts of this course can be taught in English.
Compulsory assignments
- Exercises
Further on evaluation
The re-sit examination may be given as an oral examination. The retake exam is in August.
Recommended previous knowledge
MA1201 Linear algebra and geometry.
Course materials
Will be announced at the start of the semester.
Credit reductions
| Course code | Reduction | From | To |
|---|---|---|---|
| MNFMA108 | 7.5 | ||
| MA6202 | 7.5 | AUTUMN 2007 | |
| TMA4110 | 3.0 | AUTUMN 2009 | |
| TMA4115 | 3.0 | AUTUMN 2009 |
Version: 1
Credits:
7.5 SP
Study level: Foundation courses, level I
Term no.: 1
Teaching semester: SPRING 2025
Language of instruction: Norwegian
Location: Trondheim
- Mathematics
Department with academic responsibility
Department of Mathematical Sciences
Examination
Examination arrangement: School exam
- Term Status code Evaluation Weighting Examination aids Date Time Examination system Room *
- Spring ORD School exam 100/100 D INSPERA
-
Room Building Number of candidates - Summer UTS School exam 100/100 D INSPERA
-
Room Building Number of candidates
- * The location (room) for a written examination is published 3 days before examination date. If more than one room is listed, you will find your room at Studentweb.
For more information regarding registration for examination and examination procedures, see "Innsida - Exams"