Module Code: |
H6LA |
Long Title
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Linear Algebra
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Title
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Linear Algebra
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Module Level: |
LEVEL 6 |
EQF Level: |
5 |
EHEA Level: |
Short Cycle |
Module Coordinator: |
MICHAEL BRADFORD |
Module Author: |
MICHAEL BRADFORD |
Departments: |
School of Computing
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Specifications of the qualifications and experience required of staff |
Master’s degree in mathematics, computing or cognate discipline. May have industry experience also.
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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).
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No recommendations listed |
Co-requisite Modules
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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
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Module Content & Assessment
Indicative Content |
Matrix Algebra
Motivation and Context. Linear Equations. Matrix Operations. Types of Matrices
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Matrix Algebra
Trace of a Matrix. Matrix Inversion.
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Matrix Algebra
Permutations. Determinants. Minors and Cofactors
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Vector Spaces
Definitions and examples. Linear Dependence. Basis and Dimension
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Vector Spaces
Inner Product Spaces. Norms
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Vector Spaces
Othogonalization. Linear Simultaneous Equations. Gaussian Elimination
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Linear Transformations
Properties of Linear Transformations . Matrix Representation
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Linear Transformations
Change of Basis. Eigenvalues and Eigenvectors. Characteristic and Minimal Polynomials
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Linear Transformations
Cayley-Hamilton Theorem. Singular Value Decomposition
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Introduction to Geometric Algebra
Motivation and Context. Axioms of Geometric Algebra. Vectors and Scalars. The Geometric Product
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Introduction to Geometric Algebra
Analytical Geometry. Multivectors
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Introduction to Geometric Algebra
Linear Transformations. Applications
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Assessment Breakdown | % |
Coursework | 40.00% |
End of Module Assessment | 60.00% |
AssessmentsFull 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. |
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No End of Module 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.
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Reassessment Description The repeat strategy for this module is an examination. All learning outcomes will be assessed in the repeat exam.
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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 |
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Strang, G.. (2016), Introduction to Linear Algebra (5th ed), Wellesley-Cambridge Press.
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Lipschutz, S. & Lipson M.. (2012), Schaum's Outline of Linear Algebra (5th ed), McGraw Hill Education.
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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 |
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Datta, K. B.. (2016), Matrix and Linear Algebra: Aided with MATLAB (3rd ed), Prentice-Hall of India Pvt Ltd.
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Anton, H.. (2013), Elementary Linear Algebra (11th ed), Wiley.
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Hestenes, D.. (2008), New Foundations for Classical Mechanics (2nd ed), Springer.
| This module does not have any article/paper resources |
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Other Resources |
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[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/.
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[Website], University of Cambridge, Geometric
Algebra Lecture Series by Chris Doran @
http://geometry.mrao.cam.ac.uk/2016/10/g
eometric-algebra-2016/.
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