Module Code: H6LA
Long Title Linear Algebra
Title Linear Algebra
Module Level: LEVEL 6
EQF Level: 5
EHEA Level: Short Cycle
Credits: 5
Module Coordinator: MICHAEL BRADFORD
Module Author: MICHAEL BRADFORD
Departments: School of Computing
Specifications of the qualifications and experience required of staff


Master’s degree in mathematics, computing or cognate discipline. May have industry experience also.
 

Learning Outcomes
On successful completion of this module the learner will be able to:
# Learning Outcome Description
LO1 Apply matrix algebra operations and investigate properties of matrices.
LO2 Define vector spaces and describe the structure of vector spaces in terms of linear independence, basis, and dimension.
LO3 Examine qualitative and quantitative aspects (e.g., such as norm and orthogonality) of vector spaces when presented as inner product spaces.
LO4 Determine if a system of linear simultaneous equations can be solved and if so provide a solution.
LO5 Describe the properties of linear transformations and determine how such transformations can be represented by matrices.
LO6 Investigate and apply coordinate free representations of linear transformations using Geometric Algebra.
Dependencies
Module Recommendations

This is prior learning (or a practical skill) that is required before enrolment on this module. While the prior learning is expressed as named NCI module(s) it also allows for learning (in another module or modules) which is equivalent to the learning specified in the named module(s).

No recommendations listed
Co-requisite Modules
No Co-requisite modules listed
Entry requirements

Learners should have attained the knowledge, skills and competence gained from stage 1 of the BSc (Hons) in Data Science

 

Module Content & Assessment

Indicative Content
Matrix Algebra
Motivation and Context. Linear Equations. Matrix Operations. Types of Matrices
Matrix Algebra
Trace of a Matrix. Matrix Inversion.
Matrix Algebra
Permutations. Determinants. Minors and Cofactors
Vector Spaces
Definitions and examples. Linear Dependence. Basis and Dimension
Vector Spaces
Inner Product Spaces. Norms
Vector Spaces
Othogonalization. Linear Simultaneous Equations. Gaussian Elimination
Linear Transformations
Properties of Linear Transformations . Matrix Representation
Linear Transformations
Change of Basis. Eigenvalues and Eigenvectors. Characteristic and Minimal Polynomials
Linear Transformations
Cayley-Hamilton Theorem. Singular Value Decomposition
Introduction to Geometric Algebra
Motivation and Context. Axioms of Geometric Algebra. Vectors and Scalars. The Geometric Product
Introduction to Geometric Algebra
Analytical Geometry. Multivectors
Introduction to Geometric Algebra
Linear Transformations. Applications
Assessment Breakdown%
Coursework40.00%
End of Module Assessment60.00%

Assessments

Full Time

Coursework
Assessment Type: Continuous Assessment % of total: Non-Marked
Assessment Date: n/a Outcome addressed: 1,2,3,4,5,6
Non-Marked: Yes
Assessment Description:
Ongoing independent and group class activities and feedback.
Assessment Type: Continuous Assessment % of total: 40
Assessment Date: n/a Outcome addressed: 1,2,3,4,5,6
Non-Marked: No
Assessment Description:
A comprehensive set of questions relating to Matrix Algebra, Vector Spaces, Linear Transformations, and Geometric Algebra.
Assessment Type: Easter Examination % of total: 60
Assessment Date: n/a Outcome addressed: 1,2,3,4,5,6
Non-Marked: No
Assessment Description:
Written examination with questions from all module topic areas.
No End of Module Assessment
No Workplace Assessment
Reassessment Requirement
Repeat examination
Reassessment of this module will consist of a repeat examination. It is possible that there will also be a requirement to be reassessed in a coursework element.
Reassessment Description
The repeat strategy for this module is an examination. All learning outcomes will be assessed in the repeat exam.

NCIRL reserves the right to alter the nature and timings of assessment

 

Module Workload

Module Target Workload Hours 0 Hours
Workload: Full Time
Workload Type Workload Description Hours Frequency Average Weekly Learner Workload
Lecture Classroom & Demonstrations (hours) 24 Per Semester 2.00
Tutorial Other hours (Practical/Tutorial) 12 Per Semester 1.00
Independent Learning Independent learning (hours) 89 Per Semester 7.42
Total Weekly Contact Hours 3.00
 

Module Resources

Recommended Book Resources
  • Strang, G.. (2016), Introduction to Linear Algebra (5th ed), Wellesley-Cambridge Press.
  • Lipschutz, S. & Lipson M.. (2012), Schaum's Outline of Linear Algebra (5th ed), McGraw Hill Education.
  • Dorst, L., Fontijne D. & Mann S.. (2009), Geometric Algebra for Computer Science: An Object-Oriented Approach to Geometry (2nd ed), Morgan Kaufmann.
Supplementary Book Resources
  • Datta, K. B.. (2016), Matrix and Linear Algebra: Aided with MATLAB (3rd ed), Prentice-Hall of India Pvt Ltd.
  • Anton, H.. (2013), Elementary Linear Algebra (11th ed), Wiley.
  • Hestenes, D.. (2008), New Foundations for Classical Mechanics (2nd ed), Springer.
This module does not have any article/paper resources
Other Resources
  • [Website], MIT Open Course Ware, Massachusetts Institute of Technology. Linear Algebra Lecture Series by Gilbert Strang @ https://ocw.mit.edu/courses/mathematics/ 18-06-linear-algebra-spring-2010/.
  • [Website], University of Cambridge, Geometric Algebra Lecture Series by Chris Doran @ http://geometry.mrao.cam.ac.uk/2016/10/g eometric-algebra-2016/.
Discussion Note: