Linear Algebra, 7.5 credits

Main field of study

Course level

Advancement level

Course offered for

• Bachelor´s Programme in Statistics and Data Analysis

Intended learning outcomes

The student will learn basic mathematical concepts and methods in linear algebra that are used by statisticians. The course objective is for the student to be able to read and understand linear algebra in scientific statistical texts, and to be able to conduct logical reasoning and linear algebra calculations.

This includes that the student will
- be able to solve systems of linear equations.
- know the concept of a vector in arbitrary dimenstion.
- be able to calculate scalar products and projections of vectors.
- know the concepts of a matrix and be able to perform matrix calculations.
- be able to calculate determinants and know what the determinant say about linear dependencies.
- know examples of linear maps and how to represent these by matrices.
- know the concepts of basis and coordinates, and be able to use orthogonal matrices for change of bases.
- be able to determine eigenvalues and eigenvectors.
- be able to diagonalize symmetric matrices and use this on quadratic forms.
- be able to use the method of least squares and know about the geometrical interpretation.

Course content

The following be treated in the course.
- Linear systems of equations: succesive elimination and substitution, possible solutions, geometrical interpretation.
- Matrices: multiplication, transpose, rank, trace, inverse, easy equations.
- Vectors: geometrical vectors, scalar product, projections, coordinates, linear combinations, linear independencies/dependencies.
- Bases: orthonormal bases, change of bases, orthogonal matrices, Gram-Schmidt process.
- Determinants: definition, calculation of orders 2 and 3, relation to linear dependencies and systems of equations.
- Linear maps: geometrical examples, matrix representation.
- Diagonalization: eigenvalues, eigenvectors, spectral decomposition, calculations for matrices of order 2 and 3.
- Quadratic forms: matrix representation, diagonalization.
- Method of least squares: overdetermined systems of equations, geometrical interpretation, curve-fitting.

Teaching and working methods

The teaching will be lectures, where concepts and methods will be presented, and lessons with the possibility for individual help in the students own work with exercises. Self-studies is necessary as a complement to the scheduled teaching.

Examination

A control exam that is not obligatory.
A written exam.

Grades

Other information

Planning and implementation of a course must take its starting point in the wording of the syllabus. The course evaluation included in each course must therefore take up the question how well the course agrees with the syllabus. The course is carried out in such a way that both men´s and women´s experience and knowledge is made visible and developed.

Department