Linear Algebra II
Syllabus, Bachelor's level, 1MA024
- Code
- 1MA024
- Education cycle
- First cycle
- Main field(s) of study and in-depth level
- Mathematics G1F
- Grading system
- Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
- Finalised by
- The Faculty Board of Science and Technology, 27 April 2010
- Responsible department
- Department of Mathematics
Entry requirements
Linear Algebra and Geometry I, Single Variable Calculus
Learning outcomes
In order to pass the course (grade 3) the student should
Content
Linear spaces: subspaces, linear span, linear dependence, basis, dimension, change of bases. Matrices: rank, column space and row space. Determinants of arbitrary order. Linear transformations: their matrix and its dependence on the bases, composition and inverse, range and nullspace, the dimension theorem. Euclidean spaces: inner product, the Cauchy-Schwarz inequality, orthogonality, ON-basis, orthogonalisation, orthogonal projection, isometry. Quadratic forms: diagonalisation, Sylvester's law of inertia. Spectral theory: eigenvalues, eigenvectors, eigenspaces, characteristic polynomial, diagonalisability, the spectral theorem, second degree surfaces. Systems of linear ordinary differential equations.
Instruction
Lectures and problem solving sessions.
Assessment
Written examination at the end of the course. Moreover, compulsory assignments may be given during the course.
Reading list
- Reading list valid from Autumn 2024
- Reading list valid from Autumn 2023
- Reading list valid from Autumn 2022
- Reading list valid from Spring 2022
- Reading list valid from Autumn 2021
- Reading list valid from Spring 2020
- Reading list valid from Autumn 2019
- Reading list valid from Autumn 2018
- Reading list valid from Spring 2016
- Reading list valid from Autumn 2013
- Reading list valid from Autumn 2012
- Reading list valid from Spring 2012
- Reading list valid from Autumn 2010, version 2
- Reading list valid from Autumn 2010, version 1
- Reading list valid from Spring 2009, version 3
- Reading list valid from Spring 2009, version 2
- Reading list valid from Spring 2009, version 1
- Reading list valid from Autumn 2007