Module Content

The module covers
  • vector spaces,
  • linear transformations,
  • orthogonality,
  • and explains how these topics can be applied to
  • signal processing,
  • computer graphics,
  • data fitting.

Module Coordinates

  • Lecturer: Tobias Rossmann
  • Lectures: Tuesday 1-2pm in AC202, Friday 12 noon-1pm in AC214.
  • Tutorials: Thursday 12 noon-1pm in IT206.
  • Recomended text: David C. Lay, "Linear Algebra and Its Applications", Fourth Edition, Pearson, 2012
  • Problem sheet: available here.
  • Module Website: Information and module documents will be posted to this site, which is linked from the Blackboard MA313 Linear Algebra pages. Blackboard will also be used for announcements and for posting grades.

Module Assessment

  • End of semester examination: 50%.
  • Continuous assessment: 30%.
  • Communications skils: 20%.

Supplementary Material and News

A model paper is avaialble here.

Clicker opinion polling may be used in some lectures.

Lecture Notes

Lecture Notes
(click on number)

Lecture Summaries
1
Introduction and course overview. Definition of a vector space. Rn is a vector space.
2
Basic properties of vector spaces. Further examples: discrete signals, polynomials, and function spaces.
3
Subspaces of a vector space.
4
Linear combinations and spans. Spaces of continuous functions.
5
Null spaces and row reduction. Column spaces.
6
Linear transformations. Matrices and linear transformations from Rn to Rm.
7
Linear transformations arising from calculus and in signal processing. Essay topics.
8
Linear independence and bases.
9
Finitely generated vector spaces have bases. Finding bases of null spaces.
10
First test.
11
Coordinate vectors and mappings.
12
Isomorphisms. Computer graphics.
13
Dimension.
14
The Rank-Nullity Theorem.
15
More about ranks. Matrices and linear transformations.
16
Second test. Guidelines for the essay.
17
Inner product, length, orthogonality, Pythagorean theorem, orthogonal complements of subspaces.
18
Orthogonal projections and bases.
19
The Gram-Schmidt process. Orthogonal matrices.
20
Orthogonal matrices. Best Approximation Theorem.
21
Least-squares problems.
22
Third test.
23
Communication skills presentations.
24
Revision Q&A.