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, 15 March 2007
- 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 be able to
Higher grades, 4 or 5, require a higher level of proficiency. The student should be able to solve problems of greater complexity, i.e. problems requiring a combination of ideas and methods for their solution, and be able to give a more detailed account of the proofs of important theorems and by examples and counter-examples be able to motivate the scope of various results. Requirements concerning the student's ability to present mathematical arguments and reasoning are greater.
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