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, 2 May 2016
- Responsible department
- Department of Mathematics
Entry requirements
Single Variable Calculus. Linear Algebra and Geometry I or Algebra and Geometry.
Learning outcomes
In order to pass the course (grade 3) the student should
- be able to give an account of and use basic vector space concepts such as linear space, linear dependence, basis, dimension, linear transformation;
- be able to give an account of and use basic concepts in the theory of finite dimensional Euclidean spaces;
- be able to compute determinants of arbitrary order;
- be familiar with the concepts of eigenvalue, eigenspace and eigenvector and know how to compute these objects;
- know the spectral theorem for symmetric operators and know how to diagonalise quadratic forms in ON-bases;
- know how to solve a system of linear differential equations with constant coefficients;
- be able to formulate important results and theorems covered by the course;
- be able to use the theory, methods and techniques of the course to solve mathematical problems;
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 and assignments 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