Last modified: 14 Nov 2025 11:46
Linear algebra is the study of vector spaces and linear maps between them and it is a central subject within mathematics.
It provides foundations for almost all branches of mathematics and sciences in general. The techniques are used in engineering, physics, computer science, economics and others. For example, special relativity and quantum mechanics are formulated within the framework of linear algebra.
The two courses Linear Algebra I and II aim at providing a solid foundation of the subject.
| Study Type | Undergraduate | Level | 2 |
|---|---|---|---|
| Term | Second Term | Credit Points | 15 credits (7.5 ECTS credits) |
| Campus | Aberdeen | Sustained Study | No |
| Co-ordinators |
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This is the second part of the two parts course on linear algebra. The whole course contains the following topics:
* Fields
* Vector spaces
* Linear maps
* Matrices
* Linear equations
* Eigenvalues and eigenvectors
Syllabus
Information on contact teaching time is available from the course guide.
| Assessment Type | Summative | Weighting | 25 | |
|---|---|---|---|---|
| Assessment Weeks | Feedback Weeks | |||
| Feedback |
Group Exercise Creation |
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| Knowledge Level | Thinking Skill | Outcome |
|---|---|---|
| Conceptual | Analyse | Be able to prove basic results about linear transformations and their properties. |
| Conceptual | Understand | Understand the definition and properties of the ring of polynomials with coefficients in a field. |
| Procedural | Apply | Be able to calculate determinants and find the inverse of a matrix. |
| Assessment Type | Summative | Weighting | 20 | |
|---|---|---|---|---|
| Assessment Weeks | Feedback Weeks | |||
| Feedback |
Learning Journal |
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| Knowledge Level | Thinking Skill | Outcome |
|---|---|---|
| Conceptual | Analyse | Be able to prove basic results about linear transformations and their properties. |
| Conceptual | Apply | Be able to state and apply the Cayley-Hamilton Theorem and the Spectral Theorem. |
| Conceptual | Apply | Be able to find the Jordan normal form of a matrix. |
| Conceptual | Understand | Understand the definition and properties of the ring of polynomials with coefficients in a field. |
| Factual | Remember | State the definition of a factor space. |
| Procedural | Apply | Be able to calculate eigenvalues and eigenspaces. |
| Procedural | Apply | Be able to calculate determinants and find the inverse of a matrix. |
| Procedural | Apply | Be able to calculate the minimal polynomial and characteristic polynomial. |
| Assessment Type | Summative | Weighting | 15 | |
|---|---|---|---|---|
| Assessment Weeks | Feedback Weeks | |||
| Feedback |
10 x Weekly Quizzes |
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| Knowledge Level | Thinking Skill | Outcome |
|---|---|---|
| Conceptual | Analyse | Be able to prove basic results about linear transformations and their properties. |
| Conceptual | Apply | Be able to state and apply the Cayley-Hamilton Theorem and the Spectral Theorem. |
| Conceptual | Apply | Be able to find the Jordan normal form of a matrix. |
| Conceptual | Understand | Understand the definition and properties of the ring of polynomials with coefficients in a field. |
| Factual | Remember | State the definition of a factor space. |
| Procedural | Apply | Be able to calculate eigenvalues and eigenspaces. |
| Procedural | Apply | Be able to calculate determinants and find the inverse of a matrix. |
| Procedural | Apply | Be able to calculate the minimal polynomial and characteristic polynomial. |
| Assessment Type | Summative | Weighting | 25 | |
|---|---|---|---|---|
| Assessment Weeks | Feedback Weeks | |||
| Feedback |
Group Project Report, 5 pages |
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| Knowledge Level | Thinking Skill | Outcome |
|---|---|---|
| Conceptual | Analyse | Be able to prove basic results about linear transformations and their properties. |
| Conceptual | Apply | Be able to find the Jordan normal form of a matrix. |
| Procedural | Apply | Be able to calculate eigenvalues and eigenspaces. |
| Procedural | Apply | Be able to calculate the minimal polynomial and characteristic polynomial. |
| Assessment Type | Summative | Weighting | 15 | |
|---|---|---|---|---|
| Assessment Weeks | Feedback Weeks | |||
| Feedback |
12-minute Group Project Video Presentation |
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| Knowledge Level | Thinking Skill | Outcome |
|---|---|---|
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There are no assessments for this course.
| Assessment Type | Summative | Weighting | ||
|---|---|---|---|---|
| Assessment Weeks | Feedback Weeks | |||
| Feedback |
Individual tasks will be assigned in place of group work |
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| Knowledge Level | Thinking Skill | Outcome |
|---|---|---|
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| Knowledge Level | Thinking Skill | Outcome |
|---|---|---|
| Conceptual | Apply | Be able to state and apply the Cayley-Hamilton Theorem and the Spectral Theorem. |
| Factual | Remember | State the definition of a factor space. |
| Conceptual | Apply | Be able to find the Jordan normal form of a matrix. |
| Conceptual | Understand | Understand the definition and properties of the ring of polynomials with coefficients in a field. |
| Conceptual | Analyse | Be able to prove basic results about linear transformations and their properties. |
| Procedural | Apply | Be able to calculate determinants and find the inverse of a matrix. |
| Procedural | Apply | Be able to calculate eigenvalues and eigenspaces. |
| Procedural | Apply | Be able to calculate the minimal polynomial and characteristic polynomial. |
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