# Linear Algebra, 6 credits (TNA002)

Linjär algebra, 6 hp

### Main field of study

Mathematics Applied Mathematics

First cycle

Programme course

George Baravdish

### Director of studies or equivalent

George Baravdish
Course offered for Semester Period Timetable module Language Campus VOF
6CIEN Electronics Design Engineering, M Sc in Engineering 1 (Autumn 2017) 2 - Swedish Norrköping o
6CKTS Communications, Transport and Infrastructure, M Sc in Engineering 1 (Autumn 2017) 2 - Swedish Norrköping o
6CMEN Media Technology and Engineering, M Sc in Engineering 1 (Autumn 2017) 2 - Swedish Norrköping o

### Main field of study

Mathematics, Applied Mathematics

First cycle

G1X

### Course offered for

• Electronics Design Engineering, M Sc in Engineering
• Communications, Transport and Infrastructure, M Sc in Engineering
• Media Technology and Engineering, M Sc in Engineering

### Entry requirements

Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshold requirements for progression within the programme, or corresponding.

### Intended learning outcomes

To give a unified framework for geometrical and algebraic techniques, with applications in analysis, mechanics, computer graphics, numerical analysis, mathematical statistics, control theory, linear optimization and other subjects. It is also included to develop the ability of using the mathematical language both written and oral. It is necessary for the participant to be able to

• solve systems of linear equations
• work with inner and cross product
• calculate with matrices and determinants
• calculate with vectors and coordinates in a vector space
• determine the matrix for a linear transformation and the kernel and the range for such matrices
• determine ON-basis in an inner product space
• do orthogonal projection on subspaces and to use least squares approximations
• solve problems by changing basis
• determine and to use eigenvalues and eigenvectors in different problems
• use the spectral theorem in different problems
• determine the canonical basis of quadratic forms and to use these to solve geometrical problems.
• carry out inspections of results and partial results, in order to verify that these are correct or reasonable
• solve system of linear ordinary differential equations

• ### Course content

Vectors, straight lines and planes. Linear systems of equations. Matrices and determinants. Vector spaces. Euclidean spaces.
Linear mappings. Isometric and symmetric mappings. Eigenvalues and eigenvectors. Diagonalization. Otrhogonality. Quadratic forms. Distance and approximation. System of linear ordinary differential equations

### Teaching and working methods

The course is given in the form of lectures and tutorials.

### Examination

 TEN1 Written examination U, 3, 4, 5 6 credits KTR1 Individual assignments D 0 credits UPG2 Individual assignment U, G 0 credits KTR2 Individual assignments D 0 credits

Four-grade scale, LiU, U, 3, 4, 5

### Department

Institutionen för teknik och naturvetenskap

### Director of Studies or equivalent

George Baravdish

### Examiner

George Baravdish

### Course website and other links

http://www2.itn.liu.se/utbildning/kurs/

### Education components

Preliminary scheduled hours: 87 h
Recommended self-study hours: 73 h

### Course literature

##### Compendiums

Kompendium utgivet vid ITN.

### Compendia

Kompendium utgivet vid ITN.