MATA122 Linear Algebra and Geometry 2 (4 cr)
Study level:
Intermediate studies
Grading scale:
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
Grading scale:
0-5
Evaluation criteria:
Opintojakson arvosana määräytyy kurssitentin pistemäärän ja laskuharjoitushyvitysten summan perusteella.
Language:
Finnish
Study methods:
Luennot 38h, 8 harjoituskertaa.
Teaching
8/26–8/26/2020 Exam
1/11–3/14/2021 Lectures
3/10–3/10/2021 Exam
3/24–3/24/2021 Exam
4/14–4/14/2021 Course Exam
x
Exam (4 cr)
Type:
Exam
Grading scale:
0-5
Evaluation criteria:
Opintojakson arvosana määräytyy lopputentin pistemäärän perusteella. Hyväksyttyyn arvosanaan vaaditaan vähintään puolet maksimipistemäärästä.
Language:
English, Finnish