# MA1202 - Linear Algebra with Applications

### Examination arrangement

Examination arrangement: School exam

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.

• Exercises

### Specific conditions

Compulsory activities from previous semester may be approved by the department.

### 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
More on the course
Facts

Version: 1
Credits:  7.5 SP
Study level: Foundation courses, level I

Coursework

Term no.: 1
Teaching semester:  SPRING 2023

Language of instruction: Norwegian

Location: Trondheim

Subject area(s)
• Mathematics
Contact information
Course coordinator:

Department of Mathematical Sciences

# Examination

#### Examination arrangement: School exam

Term Status code Evaluation Weighting Examination aids Date Time Examination system
Spring ORD School exam 100/100 2023-05-15 15:00
Summer UTS School exam 100/100
• * 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.
Examination

For more information regarding registration for examination and examination procedures, see "Innsida - Exams"

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