# MATA122 Linear Algebra and Geometry 2 (4 cr)

Study level:
Intermediate studies
0-5
Language:
English, Finnish
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2020-2021, 2021-2022, 2022-2023

## Description

Change of basis, eigenvalue theory, quadratic forms, abstract vector spaces and related concepts, sub-spaces, basis, dimension, linear transformations and matrices.

The contents correspond to

Lay: Linear algebra and its applications (2nd ed.) chapters 4.1-4.7, 5.1-5.4, 6.5 and 7.1-7.2.

or

Anton ja Rorres: Elementary Linear Algebra (11th ed) chapters 4-8.

## Learning outcomes

After completing the course, the student
• knows the definitions of the eigenvalues, -vectors, and -spaces of a linear mapping and square matrix, and can find these for a given mapping and matrix
• is able to examine whether a given square matrix is ​​diagonalizable
• is able to apply a quadratic form associated with a symmetric matrix to identify and recognize conic sections and quadratic surfaces
• Is familiar with the definitions of symmetric linear mapping and matrix, and the importance of symmetry in finding eigenvalues and -spaces and in diagonalizing
• is familiar with the notion of least-squares solution and knows how to compute it
• can give examples of real vector spaces and linear mappings between them
• knows the connection between linear mappings between finite dimensional vector spaces and matrices and can use this connection
• can calculate how changing bases changes the vector coordinates and the matrix corresponding to the linear mapping
• is familiar with the general definition of an inner product space and is able to investigate whether a given mapping is an inner product
• is able to determine the orthogonality and orthonormality of a vector set by using the inner product
• is able to use Geogebra to familiarize with geometric concepts in the course

## Description of prerequisites

Linear algebra and geometry 1

## Study materials

Lecture notes (in Finnish)

## Completion methods

### Method 1

Evaluation criteria:
Grading is based on points from the course exam and weekly exercises
Time of teaching:
Period 3
Select all marked parts

### Method 2

Evaluation criteria:
Grading is based on points from the final exam
Select all marked parts
Parts of the completion methods
x

### Teaching (4 cr)

Type:
Participation in teaching
0-5
Evaluation criteria:
Language:
Finnish
Study methods:

Luennot 38h, 8 harjoituskertaa.

x

Type:
Exam