# Linear Algebra

Vrije Universiteit Amsterdam

## Course Description

• ### Course Name

Linear Algebra

• ### Host University

Vrije Universiteit Amsterdam

• ### Location

Amsterdam, The Netherlands

Algebra

• ### Language Level

Taught In English

• ### Course Level Recommendations

Lower

ISA offers course level recommendations in an effort to facilitate the determination of course levels by credential evaluators.We advice each institution to have their own credentials evaluator make the final decision regrading course levels.

### Hours & Credits

• ECTS Credits

6
• Recommended U.S. Semester Credits
3
• Recommended U.S. Quarter Units
4
• ### Overview

COURSE OBJECTIVE
After successfully completing this course,
- the student has a working knowledge of the concepts of matrix algebra and finite-dimensional linear algebra, such as echelon form, lu-decomposition, linear independence, determinants
- the student is familiar with the general theory of finite-dimensional vector spaces, in particular with the concepts of basis and dimension
- the student is familiar with the concepts of eigenvalues and eigenvectors, diagonalization and singular value decomposition and can apply these concepts in basic applications in discrete time dynamical systems,
- has working knowledge of the concepts of inner product spaces and matrices acting in inner product spaces, including orthogonal projections and diagonalization of symmetric matrices.

COURSE CONTENT
- systems of linear equations
- linear (in)dependence
- linear transformations and matrices
- matrix operations
- determinants
- vector spaces and subspaces
- basis and dimension
- rank of a matrix, dimension theorem
- coordinate systems and change of basis
- eigenvalues and eigenvectors
- diagonalization of matrices
- inner product, length and orthogonality
- orthogonal bases and least-squares problem
- diagonalization of symmetric matrices
- singular value decomposition

FORM OF TUITION
2 lectures and 1 exercise class per week

TYPE OF ASSESSMENT
Six bi-weekly tests (20 percent, only the best five are taken into account), a midterm exam (40 percent) and a final exam (40 percent). There is a resit. For students taking the resit the final grade is determined by the maximum of the following two numbers: 0.2 times the average of the best five tests plus 0.8 times the result of the resit and just the resit.

### Course Disclaimer

Courses and course hours of instruction are subject to change.

Some courses may require additional fees.

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